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¿cómo vas a descomponer esta expresión en fracciones?:
-((-1+x^2/(1+x^2))/sqrt(1+x^2)+(1+x/sqrt(1+x^2))^2/(x+sqrt(1+x^2)))/(x+sqrt(1+x^2))
((z-1)*((z*f*r*f)/(1+(z-1)*c*f)))/(z*r)
y+y/x-y+1/(x^2)-x
y/(y+3)^2-y/(y^2)-9
Factorizar el polinomio:
z^2+2*z+26
z^2-169/196
y+y^2/2
y*y/x-x^2+x*y/x-y^2
Descomponer al cuadrado:
y^4-y^2-13
y^4-9*y^2+5
-y^4-9*y^2-4
-y^4+y^2+1
Expresiones idénticas
pi*a^ dos /(seis *(uno -cos(l)))*tan(f)*sqrt(a^ dos +a*cos(l)/(cuatro / uno -cos(l)))
número pi multiplicar por a al cuadrado dividir por (6 multiplicar por (1 menos coseno de (l))) multiplicar por tangente de (f) multiplicar por raíz cuadrada de (a al cuadrado más a multiplicar por coseno de (l) dividir por (4 dividir por 1 menos coseno de (l)))
número pi multiplicar por a en el grado dos dividir por (seis multiplicar por (uno menos coseno de (l))) multiplicar por tangente de (f) multiplicar por raíz cuadrada de (a en el grado dos más a multiplicar por coseno de (l) dividir por (cuatro dividir por uno menos coseno de (l)))
pi*a^2/(6*(1-cos(l)))*tan(f)*√(a^2+a*cos(l)/(4/1-cos(l)))
pi*a2/(6*(1-cos(l)))*tan(f)*sqrt(a2+a*cos(l)/(4/1-cos(l)))
pi*a2/6*1-cosl*tanf*sqrta2+a*cosl/4/1-cosl
pi*a²/(6*(1-cos(l)))*tan(f)*sqrt(a²+a*cos(l)/(4/1-cos(l)))
pi*a en el grado 2/(6*(1-cos(l)))*tan(f)*sqrt(a en el grado 2+a*cos(l)/(4/1-cos(l)))
pia^2/(6(1-cos(l)))tan(f)sqrt(a^2+acos(l)/(4/1-cos(l)))
pia2/(6(1-cos(l)))tan(f)sqrt(a2+acos(l)/(4/1-cos(l)))
pia2/61-cosltanfsqrta2+acosl/4/1-cosl
pia^2/61-cosltanfsqrta^2+acosl/4/1-cosl
pi*a^2 dividir por (6*(1-cos(l)))*tan(f)*sqrt(a^2+a*cos(l) dividir por (4 dividir por 1-cos(l)))
Expresiones semejantes
pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt(a^2-a*cos(l)/(4/1-cos(l)))
pi*a^2/(6*(1+cos(l)))*tan(f)*sqrt(a^2+a*cos(l)/(4/1-cos(l)))
pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt(a^2+a*cos(l)/(4/1+cos(l)))
Expresiones con funciones
Número Pi pi
pi/(sqrt(1-x^2)*(exp(x)-log(x)))+pi*(1/x-exp(x))*asin(x)/(exp(x)-log(x))^2
pi/(10+x/2)-pi*x/(2*(10+x/2)^2)
pi*sin(pi/(z+1))/(z+1)^2
pi/(3*(1+pi^2*x^2/9))
Piecewise((-a^2*acosh(x/a)/2+x^3/(2*a*sqrt(-1+x^2/a^2))-a*x/(2*sqrt(-1+x^2/a^2)),|x^2/a^2|>1),(i*a^2*asin(x/a)/2+i*a*x*sqrt(1-x^2/a^2)/2,True))
Coseno cos
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20))
cos(x)^(2/x)*(-2*log(cos(x))/x^2-2*sin(x)/(x*cos(x)))
cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2)
cos(-x)*cos(pi+x)/(sin(-x)*sin(pi/2+x))
Tangente tan
tan(x+pi/8)/2-1/(2*tan(x+pi/8))
tan(pi/8)/(1-tan^2(pi/8))
tan(x)/(2+2*tan(x)^2)+x/2
tan(x)+coscos(x)/(sin*sin(x)+1)
tan(x/2)^4/(2*sqrt(x))+sqrt(x)*tan(x/2)^3*(2+2*tan(x/2)^2)
Raíz cuadrada sqrt
sqrt((1-x)/(1+x))*(1+x)*(-1/(2*(1+x))-(1-x)/(2*(1+x)^2))/(1-x)
sqrt(x)*(-3+5*x^4)+(x^5-3*x)/(2*sqrt(x))
sqrt(x*sqrt(a)/(5*x-3)^4)*(5*x-3)^4*(sqrt(a)/(2*(5*x-3)^4)-10*x*sqrt(a)/(5*x-3)^5)/(sqrt(a)*x)
sqrt(6-x)/(x^2-9)
sqrt((6,7×10^-11)×(7,3×10^22)/(17×10^5)+10^5)
Coseno cos
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20))
cos(x)^(2/x)*(-2*log(cos(x))/x^2-2*sin(x)/(x*cos(x)))
cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2)
cos(-x)*cos(pi+x)/(sin(-x)*sin(pi/2+x))
Coseno cos
cos(x)/(1+tan(x))+(-1-tan(x)^2)*sin(x)/(1+tan(x))^2
cos((7pi/24)+pi/8)/(√6*sin(pi/10+(3pi)/20))
cos(x)^(2/x)*(-2*log(cos(x))/x^2-2*sin(x)/(x*cos(x)))
cos(pi*x)*exp(x)/(1+pi^2)+pi*exp(x)*sin(pi*x)/(1+pi^2)
cos(-x)*cos(pi+x)/(sin(-x)*sin(pi/2+x))

Simplificación de expresiones/ Descomposición en fracciones simples/ pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt(a^2+a*cos(l)/(4/1-cos(l)))

¿Cómo vas a descomponer esta pia^2/(6(1-cos(l)))tan(f)sqrt(a^2+a*cos(l)/(4/1-cos(l))) expresión en fracciones?

Solución

Ha introducido [src]

        2                 _________________
    pi*a                 /  2    a*cos(l)  
--------------*tan(f)*  /  a  + ---------- 
6*(1 - cos(l))        \/        4 - cos(l)

\frac{\pi a^{2}}{6 \left(1 - \cos{\left(l \right)}\right)} \tan{\left(f \right)} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}}

(((pi*a^2)/((6*(1 - cos(l)))))*tan(f))*sqrt(a^2 + (a*cos(l))/(4 - cos(l)))

Simplificación general [src]

           _______________________________        
     2    / a*(-cos(l) + a*(-4 + cos(l)))         
-pi*a *  /  ----------------------------- *tan(f) 
       \/            -4 + cos(l)                  
--------------------------------------------------
                  -6 + 6*cos(l)

- \frac{\pi a^{2} \sqrt{\frac{a \left(a \left(\cos{\left(l \right)} - 4\right) - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}

-pi*a^2*sqrt(a*(-cos(l) + a*(-4 + cos(l)))/(-4 + cos(l)))*tan(f)/(-6 + 6*cos(l))

Respuesta numérica [src]

3.14159265358979*a^2*(a^2 + a*cos(l)/(4.0 - cos(l)))^0.5*tan(f)/(6.0 - 6.0*cos(l))

3.14159265358979*a^2*(a^2 + a*cos(l)/(4.0 - cos(l)))^0.5*tan(f)/(6.0 - 6.0*cos(l))

Denominador racional [src]

           _______________________________        
     2    / a*(-cos(l) + a*(-4 + cos(l)))         
-pi*a *  /  ----------------------------- *tan(f) 
       \/            -4 + cos(l)                  
--------------------------------------------------
                  -6 + 6*cos(l)

- \frac{\pi a^{2} \sqrt{\frac{a \left(a \left(\cos{\left(l \right)} - 4\right) - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}

-pi*a^2*sqrt(a*(-cos(l) + a*(-4 + cos(l)))/(-4 + cos(l)))*tan(f)/(-6 + 6*cos(l))

Unión de expresiones racionales [src]

          _____________________________       
    2    / a*(a*(4 - cos(l)) + cos(l))        
pi*a *  /  --------------------------- *tan(f)
      \/            4 - cos(l)                
----------------------------------------------
                 6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{\frac{a \left(a \left(4 - \cos{\left(l \right)}\right) + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

pi*a^2*sqrt(a*(a*(4 - cos(l)) + cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))

Combinatoria [src]

           ________________________________        
     2    / -a*(-cos(l) - 4*a + a*cos(l))          
-pi*a *  /  ------------------------------ *tan(f) 
       \/             4 - cos(l)                   
---------------------------------------------------
                  6*(-1 + cos(l))

- \frac{\pi a^{2} \sqrt{- \frac{a \left(a \cos{\left(l \right)} - 4 a - \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}

-pi*a^2*sqrt(-a*(-cos(l) - 4*a + a*cos(l))/(4 - cos(l)))*tan(f)/(6*(-1 + cos(l)))

Denominador común [src]

           _________________        
     2    /  2    a*cos(l)          
-pi*a *  /  a  + ---------- *tan(f) 
       \/        4 - cos(l)         
------------------------------------
           -6 + 6*cos(l)

- \frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \cos{\left(l \right)} - 6}

-pi*a^2*sqrt(a^2 + a*cos(l)/(4 - cos(l)))*tan(f)/(-6 + 6*cos(l))

Potencias [src]

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *tan(f)
      \/        4 - cos(l)        
----------------------------------
           6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

                  _______________________                 
                 /        / I*l    -I*l\                  
                /         |e      e    |                  
               /        a*|---- + -----|                  
      2       /     2     \ 2       2  /  /   I*f    -I*f\
pi*I*a *     /     a  + ---------------- *\- e    + e    /
            /                I*l    -I*l                  
           /                e      e                      
          /             4 - ---- - -----                  
        \/                   2       2                    
----------------------------------------------------------
          / I*f    -I*f\ /       I*l      -I*l\           
          \e    + e    /*\6 - 3*e    - 3*e    /

\frac{i \pi a^{2} \sqrt{a^{2} + \frac{a \left(\frac{e^{i l}}{2} + \frac{e^{- i l}}{2}\right)}{- \frac{e^{i l}}{2} + 4 - \frac{e^{- i l}}{2}}} \left(- e^{i f} + e^{- i f}\right)}{\left(e^{i f} + e^{- i f}\right) \left(- 3 e^{i l} + 6 - 3 e^{- i l}\right)}

pi*i*a^2*sqrt(a^2 + a*(exp(i*l)/2 + exp(-i*l)/2)/(4 - exp(i*l)/2 - exp(-i*l)/2))*(-exp(i*f) + exp(-i*f))/((exp(i*f) + exp(-i*f))*(6 - 3*exp(i*l) - 3*exp(-i*l)))

Compilar la expresión [src]

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *tan(f)
      \/        4 - cos(l)        
----------------------------------
           6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

pi*a^2*sqrt(a^2 + a*cos(l)/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))

Abrimos la expresión [src]

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *tan(f)
      \/        4 - cos(l)        
----------------------------------
          6*(1 - cos(l))

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(1 - \cos{\left(l \right)}\right)}

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *tan(f)
      \/        4 - cos(l)        
----------------------------------
           6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

pi*a^2*sqrt(a^2 + (a*cos(l))/(4 - cos(l)))*tan(f)/(6 - 6*cos(l))

Parte trigonométrica [src]

              ____________________________________            
    2        /  2                 a                   /pi    \
pi*a *      /  a  + ----------------------------- *csc|-- - f|
           /        /         1     \    /pi    \     \2     /
          /         |4 - -----------|*csc|-- - l|             
         /          |       /pi    \|    \2     /             
        /           |    csc|-- - l||                         
      \/            \       \2     //                         
--------------------------------------------------------------
                   /         6     \                          
                   |6 - -----------|*csc(f)                   
                   |       /pi    \|                          
                   |    csc|-- - l||                          
                   \       \2     //

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(- l + \frac{\pi}{2} \right)}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}

          _________________            
    2    /  2    a*cos(l)      /    pi\
pi*a *  /  a  + ---------- *cos|f - --|
      \/        4 - cos(l)     \    2 /
---------------------------------------
         (6 - 6*cos(l))*cos(f)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}

                   _____________________________________             
                  /   /     1                   a     \              
                 /  a*|----------- + 4*a - -----------|              
                /     |   /pi    \            /pi    \|              
               /      |csc|-- - l|         csc|-- - l||              
     2        /       \   \2     /            \2     //     /pi    \ 
-pi*a *      /      ----------------------------------- *csc|-- - f| 
            /                          1                    \2     / 
           /                  4 - -----------                        
          /                          /pi    \                        
         /                        csc|-- - l|                        
       \/                            \2     /                        
---------------------------------------------------------------------
                       /          1     \                            
                     6*|-1 + -----------|*csc(f)                     
                       |        /pi    \|                            
                       |     csc|-- - l||                            
                       \        \2     //

- \frac{\pi a^{2} \sqrt{\frac{a \left(4 a - \frac{a}{\csc{\left(- l + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right)}{4 - \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{6 \left(-1 + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}

                ______________________       
               /        /       2   \        
              /       a*|1 - -------|        
             /          |       2/l\|        
            /           |    sec |-||        
    2      /      2     \        \2//        
pi*a *    /      a  + --------------- *sec(f)
         /                     1             
        /               -4 + ------          
      \/                     sec(l)          
---------------------------------------------
           /      6   \    /    pi\          
           |6 - ------|*sec|f - --|          
           \    sec(l)/    \    2 /

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \frac{2}{\sec^{2}{\left(\frac{l}{2} \right)}}\right)}{-4 + \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *tan(f)
      \/        4 - cos(l)        
----------------------------------
           6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

          __________________       
    2    /  2     a*cos(l)         
pi*a *  /  a  - ----------- *tan(f)
      \/        -4 + cos(l)        
-----------------------------------
            6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

                       _________________________________________        
                      /   /             2/l\     /       2/l\\\         
                     /    |      1 - tan |-|   a*|1 - tan |-|||         
                    /     |              \2/     \        \2//|         
                   /    a*|4*a + ----------- - ---------------|         
                  /       |             2/l\            2/l\  |         
                 /        |      1 + tan |-|     1 + tan |-|  |         
     2          /         \              \2/             \2/  /         
-pi*a *        /        --------------------------------------- *tan(f) 
              /                                2/l\                     
             /                          1 - tan |-|                     
            /                                   \2/                     
           /                        4 - -----------                     
          /                                    2/l\                     
         /                              1 + tan |-|                     
       \/                                       \2/                     
------------------------------------------------------------------------
                            /            2/l\\                          
                            |     1 - tan |-||                          
                            |             \2/|                          
                          6*|-1 + -----------|                          
                            |            2/l\|                          
                            |     1 + tan |-||                          
                            \             \2//

- \frac{\pi a^{2} \sqrt{\frac{a \left(- \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4 a + \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4}} \tan{\left(f \right)}}{6 \left(\frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right)}

                ______________________        
               /            /    pi\          
              /        a*sin|l + --|          
      2      /    2         \    2 /      2   
2*pi*a *    /    a  + --------------- *sin (f)
           /                 /    pi\         
          /           4 - sin|l + --|         
        \/                   \    2 /         
----------------------------------------------
         /         /    pi\\                  
         |6 - 6*sin|l + --||*sin(2*f)         
         \         \    2 //

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \sin{\left(l + \frac{\pi}{2} \right)}}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}

                    _______________________________________       
                   /                /        2/l\\                
                  /               a*|-1 + cot |-||                
      2          /    2             \         \2//             /f\
2*pi*a *        /    a  + -------------------------------- *cot|-|
               /                        /            2/l\\     \2/
              /                         |    -1 + cot |-||        
             /            /       2/l\\ |             \2/|        
            /             |1 + cot |-||*|4 - ------------|        
           /              \        \2// |           2/l\ |        
          /                             |    1 + cot |-| |        
        \/                              \            \2/ /        
------------------------------------------------------------------
                             /      /        2/l\\\               
                             |    6*|-1 + cot |-|||               
              /        2/f\\ |      \         \2//|               
              |-1 + cot |-||*|6 - ----------------|               
              \         \2// |             2/l\   |               
                             |      1 + cot |-|   |               
                             \              \2/   /

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\left(- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\cot^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \cot{\left(\frac{f}{2} \right)}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \left(\cot^{2}{\left(\frac{f}{2} \right)} - 1\right)}

            _________________        
      2    /  2    a*cos(l)      2   
2*pi*a *  /  a  + ---------- *sin (f)
        \/        4 - cos(l)         
-------------------------------------
       (6 - 6*cos(l))*sin(2*f)

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \sin{\left(2 f \right)}}

                  ___________________________            
                 /        /         2      \             
                /       a*|1 - ------------|             
               /          |       2/pi   l\|             
              /           |    csc |-- - -||             
    2        /      2     \        \2    2//     /pi    \
pi*a *      /      a  + -------------------- *csc|-- - f|
           /                        1            \2     /
          /               -4 + -----------               
         /                        /pi    \               
        /                      csc|-- - l|               
      \/                          \2     /               
---------------------------------------------------------
                 /         6     \                       
                 |6 - -----------|*csc(f)                
                 |       /pi    \|                       
                 |    csc|-- - l||                       
                 \       \2     //

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \frac{2}{\csc^{2}{\left(- \frac{l}{2} + \frac{\pi}{2} \right)}}\right)}{-4 + \frac{1}{\csc{\left(- l + \frac{\pi}{2} \right)}}}} \csc{\left(- f + \frac{\pi}{2} \right)}}{\left(6 - \frac{6}{\csc{\left(- l + \frac{\pi}{2} \right)}}\right) \csc{\left(f \right)}}

                _____________________________        
               /        /         2/pi   l\\         
              /       a*|1 - 2*sin |-- + -||         
      2      /    2     \          \2    2//     2   
2*pi*a *    /    a  + ---------------------- *sin (f)
           /                     /    pi\            
          /              -4 + sin|l + --|            
        \/                       \    2 /            
-----------------------------------------------------
             /         /    pi\\                     
             |6 - 6*sin|l + --||*sin(2*f)            
             \         \    2 //

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \sin^{2}{\left(\frac{l}{2} + \frac{\pi}{2} \right)}\right)}{\sin{\left(l + \frac{\pi}{2} \right)} - 4}} \sin^{2}{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(2 f \right)}}

            ________________________       
           /        /         2/l\\        
          /       a*|1 - 2*cos |-||        
    2    /    2     \          \2//        
pi*a *  /    a  + ----------------- *tan(f)
      \/             -4 + cos(l)           
-------------------------------------------
                6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

               _______________________________________         
              /   /           /    pi\      /    pi\\          
             /  a*|4*a - a*sin|l + --| + sin|l + --||          
     2      /     \           \    2 /      \    2 //     2    
-pi*a *    /    ------------------------------------- *sin (f) 
          /                       /    pi\                     
         /                 4 - sin|l + --|                     
       \/                         \    2 /                     
---------------------------------------------------------------
                   /        /    pi\\                          
                 3*|-1 + sin|l + --||*sin(2*f)                 
                   \        \    2 //

- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \sin{\left(l + \frac{\pi}{2} \right)} + 4 a + \sin{\left(l + \frac{\pi}{2} \right)}\right)}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin^{2}{\left(f \right)}}{3 \left(\sin{\left(l + \frac{\pi}{2} \right)} - 1\right) \sin{\left(2 f \right)}}

                       ___________________________________________ 
                      /   /              2/l\     /        2/l\\\  
                     /    |      -1 + cot |-|   a*|-1 + cot |-|||  
                    /     |               \2/     \         \2//|  
                   /    a*|4*a + ------------ - ----------------|  
                  /       |             2/l\             2/l\   |  
                 /        |      1 + cot |-|      1 + cot |-|   |  
     2          /         \              \2/              \2/   /  
-pi*a *        /        -----------------------------------------  
              /                                  2/l\              
             /                           -1 + cot |-|              
            /                                     \2/              
           /                         4 - ------------              
          /                                     2/l\               
         /                               1 + cot |-|               
       \/                                        \2/               
-------------------------------------------------------------------
                      /             2/l\\                          
                      |     -1 + cot |-||                          
                      |              \2/|                          
                    6*|-1 + ------------|*cot(f)                   
                      |            2/l\ |                          
                      |     1 + cot |-| |                          
                      \             \2/ /

- \frac{\pi a^{2} \sqrt{\frac{a \left(- \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4 a + \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}\right)}{- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4}}}{6 \left(\frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} - 1\right) \cot{\left(f \right)}}

                  _______________________________________
                 /                /        2/l\\         
                /               a*|-1 + cot |-||         
    2          /    2             \         \2//         
pi*a *        /    a  + -------------------------------- 
             /                        /            2/l\\ 
            /                         |    -1 + cot |-|| 
           /            /       2/l\\ |             \2/| 
          /             |1 + cot |-||*|4 - ------------| 
         /              \        \2// |           2/l\ | 
        /                             |    1 + cot |-| | 
      \/                              \            \2/ / 
---------------------------------------------------------
              /      /        2/l\\\                     
              |    6*|-1 + cot |-|||                     
              |      \         \2//|                     
              |6 - ----------------|*cot(f)              
              |             2/l\   |                     
              |      1 + cot |-|   |                     
              \              \2/   /

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\left(- \frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\cot^{2}{\left(\frac{l}{2} \right)} + 1\right)}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}

              ______________________       
             /            /    pi\         
            /        a*sin|l + --|         
    2      /    2         \    2 /         
pi*a *    /    a  + --------------- *sin(f)
         /                 /    pi\        
        /           4 - sin|l + --|        
      \/                   \    2 /        
-------------------------------------------
      /         /    pi\\    /    pi\      
      |6 - 6*sin|l + --||*sin|f + --|      
      \         \    2 //    \    2 /

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \sin{\left(l + \frac{\pi}{2} \right)}}{4 - \sin{\left(l + \frac{\pi}{2} \right)}}} \sin{\left(f \right)}}{\left(6 - 6 \sin{\left(l + \frac{\pi}{2} \right)}\right) \sin{\left(f + \frac{\pi}{2} \right)}}

           _____________________________        
     2    / a*(4*a - a*cos(l) + cos(l))         
-pi*a *  /  --------------------------- *tan(f) 
       \/            4 - cos(l)                 
------------------------------------------------
                6*(-1 + cos(l))

- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \cos{\left(l \right)} + 4 a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}

               ___________________________        
              /   /  1              a   \         
             /  a*|------ + 4*a - ------|         
     2      /     \sec(l)         sec(l)/         
-pi*a *    /    ------------------------- *sec(f) 
          /                   1                   
         /              4 - ------                
       \/                   sec(l)                
--------------------------------------------------
             /       1   \    /    pi\            
           6*|-1 + ------|*sec|f - --|            
             \     sec(l)/    \    2 /

- \frac{\pi a^{2} \sqrt{\frac{a \left(4 a - \frac{a}{\sec{\left(l \right)}} + \frac{1}{\sec{\left(l \right)}}\right)}{4 - \frac{1}{\sec{\left(l \right)}}}} \sec{\left(f \right)}}{6 \left(-1 + \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}

          __________________              
    2    /  2     a*cos(l)                
pi*a *  /  a  - ----------- *sec(f)*sin(f)
      \/        -4 + cos(l)               
------------------------------------------
               6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \sin{\left(f \right)} \sec{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

              ________________________       
             /        /         2/l\\        
            /       a*|1 - 2*cos |-||        
      2    /    2     \          \2//     /f\
2*pi*a *  /    a  + ----------------- *tan|-|
        \/             -4 + cos(l)        \2/
---------------------------------------------
         /       2/f\\                       
         |1 - tan |-||*(6 - 6*cos(l))        
         \        \2//

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(\frac{f}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{f}{2} \right)}\right) \left(6 - 6 \cos{\left(l \right)}\right)}

          _________________       
    2    /  2    a*cos(l)         
pi*a *  /  a  + ---------- *sin(f)
      \/        4 - cos(l)        
----------------------------------
      (6 - 6*cos(l))*cos(f)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}

           ______________________________        
     2    / a*(-cos(l) - 4*a + a*cos(l))         
-pi*a *  /  ---------------------------- *tan(f) 
       \/           -4 + cos(l)                  
-------------------------------------------------
                 6*(-1 + cos(l))

- \frac{\pi a^{2} \sqrt{\frac{a \left(a \cos{\left(l \right)} - 4 a - \cos{\left(l \right)}\right)}{\cos{\left(l \right)} - 4}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}

           _____________________________             
     2    / a*(4*a - a*cos(l) + cos(l))     /    pi\ 
-pi*a *  /  --------------------------- *cos|f - --| 
       \/            4 - cos(l)             \    2 / 
-----------------------------------------------------
                6*(-1 + cos(l))*cos(f)

- \frac{\pi a^{2} \sqrt{\frac{a \left(- a \cos{\left(l \right)} + 4 a + \cos{\left(l \right)}\right)}{4 - \cos{\left(l \right)}}} \cos{\left(f - \frac{\pi}{2} \right)}}{6 \left(\cos{\left(l \right)} - 1\right) \cos{\left(f \right)}}

            ________________________            
           /        /         2/l\\             
          /       a*|1 - 2*cos |-||             
    2    /    2     \          \2//     /    pi\
pi*a *  /    a  + ----------------- *cos|f - --|
      \/             -4 + cos(l)        \    2 /
------------------------------------------------
             (6 - 6*cos(l))*cos(f)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \cos{\left(f - \frac{\pi}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}

                        ________________________________
                       /        /                    2\ 
                      /         |      /        2/l\\ | 
                     /          |    2*|-1 + cot |-|| | 
                    /           |      \         \4// | 
                   /          a*|1 - -----------------| 
                  /             |                   2 | 
                 /              |      /       2/l\\  | 
                /               |      |1 + cot |-||  | 
    2          /          2     \      \        \4//  / 
pi*a *        /          a  + ------------------------- 
             /                                 2/l\     
            /                          -1 + cot |-|     
           /                                    \2/     
          /                       -4 + ------------     
         /                                    2/l\      
        /                              1 + cot |-|      
      \/                                       \2/      
--------------------------------------------------------
             /      /        2/l\\\                     
             |    6*|-1 + cot |-|||                     
             |      \         \2//|                     
             |6 - ----------------|*cot(f)              
             |             2/l\   |                     
             |      1 + cot |-|   |                     
             \              \2/   /

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(- \frac{2 \left(\cot^{2}{\left(\frac{l}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{l}{4} \right)} + 1\right)^{2}} + 1\right)}{\frac{\cot^{2}{\left(\frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} - 4}}}{\left(- \frac{6 \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right) \cot{\left(f \right)}}

                  ______________________________________       
                 /                /       2/l\\                
                /               a*|1 - tan |-||                
    2          /    2             \        \2//                
pi*a *        /    a  + ------------------------------- *tan(f)
             /                        /           2/l\\        
            /                         |    1 - tan |-||        
           /            /       2/l\\ |            \2/|        
          /             |1 + tan |-||*|4 - -----------|        
         /              \        \2// |           2/l\|        
        /                             |    1 + tan |-||        
      \/                              \            \2//        
---------------------------------------------------------------
                            /       2/l\\                      
                          6*|1 - tan |-||                      
                            \        \2//                      
                      6 - ---------------                      
                                   2/l\                        
                            1 + tan |-|                        
                                    \2/

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\left(- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\tan^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}

            __________________________       
    2      /  2            a                 
pi*a *    /  a  + ------------------- *sec(f)
         /        /      1   \               
        /         |4 - ------|*sec(l)        
      \/          \    sec(l)/               
---------------------------------------------
           /      6   \    /    pi\          
           |6 - ------|*sec|f - --|          
           \    sec(l)/    \    2 /

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(l \right)}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \sec{\left(f - \frac{\pi}{2} \right)}}

                        _______________________________       
                       /        /                   2\        
                      /         |      /       2/l\\ |        
                     /          |    2*|1 - tan |-|| |        
                    /           |      \        \4// |        
                   /          a*|1 - ----------------|        
                  /             |                  2 |        
                 /              |     /       2/l\\  |        
                /               |     |1 + tan |-||  |        
    2          /          2     \     \        \4//  /        
pi*a *        /          a  + ------------------------ *tan(f)
             /                                2/l\            
            /                          1 - tan |-|            
           /                                   \2/            
          /                       -4 + -----------            
         /                                    2/l\            
        /                              1 + tan |-|            
      \/                                       \2/            
--------------------------------------------------------------
                           /       2/l\\                      
                         6*|1 - tan |-||                      
                           \        \2//                      
                     6 - ---------------                      
                                  2/l\                        
                           1 + tan |-|                        
                                   \2/

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \left(- \frac{2 \left(1 - \tan^{2}{\left(\frac{l}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{l}{4} \right)} + 1\right)^{2}} + 1\right)}{\frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} - 4}} \tan{\left(f \right)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}

            __________________________       
    2      /  2            a                 
pi*a *    /  a  + ------------------- *sec(f)
         /        /      1   \               
        /         |4 - ------|*sec(l)        
      \/          \    sec(l)/               
---------------------------------------------
             /      6   \                    
             |6 - ------|*csc(f)             
             \    sec(l)/

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a}{\left(4 - \frac{1}{\sec{\left(l \right)}}\right) \sec{\left(l \right)}}} \sec{\left(f \right)}}{\left(6 - \frac{6}{\sec{\left(l \right)}}\right) \csc{\left(f \right)}}

                    ______________________________________       
                   /                /       2/l\\                
                  /               a*|1 - tan |-||                
      2          /    2             \        \2//             /f\
2*pi*a *        /    a  + ------------------------------- *tan|-|
               /                        /           2/l\\     \2/
              /                         |    1 - tan |-||        
             /            /       2/l\\ |            \2/|        
            /             |1 + tan |-||*|4 - -----------|        
           /              \        \2// |           2/l\|        
          /                             |    1 + tan |-||        
        \/                              \            \2//        
-----------------------------------------------------------------
                             /      /       2/l\\\               
                             |    6*|1 - tan |-|||               
               /       2/f\\ |      \        \2//|               
               |1 - tan |-||*|6 - ---------------|               
               \        \2// |             2/l\  |               
                             |      1 + tan |-|  |               
                             \              \2/  /

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\left(- \frac{1 - \tan^{2}{\left(\frac{l}{2} \right)}}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 4\right) \left(\tan^{2}{\left(\frac{l}{2} \right)} + 1\right)}} \tan{\left(\frac{f}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{f}{2} \right)}\right) \left(- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6\right)}

          _________________              
    2    /  2    a*cos(l)                
pi*a *  /  a  + ---------- *sec(f)*sin(f)
      \/        4 - cos(l)               
-----------------------------------------
               6 - 6*cos(l)

\frac{\pi a^{2} \sqrt{a^{2} + \frac{a \cos{\left(l \right)}}{4 - \cos{\left(l \right)}}} \sin{\left(f \right)} \sec{\left(f \right)}}{6 - 6 \cos{\left(l \right)}}

              ________________________       
             /        /         2/l\\        
            /       a*|1 - 2*cos |-||        
      2    /    2     \          \2//     /f\
2*pi*a *  /    a  + ----------------- *cot|-|
        \/             -4 + cos(l)        \2/
---------------------------------------------
        /        2/f\\                       
        |-1 + cot |-||*(6 - 6*cos(l))        
        \         \2//

\frac{2 \pi a^{2} \sqrt{a^{2} + \frac{a \left(1 - 2 \cos^{2}{\left(\frac{l}{2} \right)}\right)}{\cos{\left(l \right)} - 4}} \cot{\left(\frac{f}{2} \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \left(\cot^{2}{\left(\frac{f}{2} \right)} - 1\right)}

          __________________       
    2    /  2     a*cos(l)         
pi*a *  /  a  - ----------- *sin(f)
      \/        -4 + cos(l)        
-----------------------------------
       (6 - 6*cos(l))*cos(f)

\frac{\pi a^{2} \sqrt{a^{2} - \frac{a \cos{\left(l \right)}}{\cos{\left(l \right)} - 4}} \sin{\left(f \right)}}{\left(6 - 6 \cos{\left(l \right)}\right) \cos{\left(f \right)}}

pi*a^2*sqrt(a^2 - a*cos(l)/(-4 + cos(l)))*sin(f)/((6 - 6*cos(l))*cos(f))

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¿Cómo vas a descomponer esta pi*a^2/(6*(1-cos(l)))*tan(f)*sqrt(a^2+a*cos(l)/(4/1-cos(l))) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta pia^2/(6(1-cos(l)))tan(f)sqrt(a^2+a*cos(l)/(4/1-cos(l))) expresión en fracciones?