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¿cómo vas a descomponer esta expresión en fracciones?:
1/(a*x-1)-1/(a*x+1)
(z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
1/(3*sqrt(1-x^2/9))
(a^3+a)/(a^4+a)
Factorizar el polinomio:
z^2-2*z+10
z^3+8*i
x^8+y^8
x^5-3*x
Descomponer al cuadrado:
-y^4-y^2-3
y^4+y^2-3
y^4+y^2-15
-y^4-y^2-11
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
Piecewise((-acosh(1/x)+1/(x*sqrt(-1+x^(-2)))-x/sqrt(-1+x^(-2)),1/|x^2|>1),(i*asin(1/x)+i*x/sqrt(1-1/x^2)-i/(x*sqrt(1-1/x^2)),True))
pi/(2*3^(7/2))-pi/3^(9/2)+1/144
pi*(2*cos(2x-1))/((tg(pi*x)^2)*(cos(pi*x)^2))
Piecewise((-i*a*acosh(x*sqrt(b)/sqrt(a))/(2*sqrt(b))-i*x*sqrt(a)/(2*sqrt(-1+b*x^2/a))+i*b*x^3/(2*sqrt(a)*sqrt(-1+b*x^2/a)),|b*x^2/a|>1),(a*asin(x*sqrt(b)/sqrt(a))/(2*sqrt(b))+x*sqrt(a)*sqrt(1-b*x^2/a)/2,True))
Piecewise((0,k=0),(-cos((k*pi)*x)/(pi*k),True))/l
Coseno cos
cos((\pi)/(2)+a)cos(\pi-a)+sin((3\pi)/(2)+a)sin(\pi+a)
cos(4*a)/(cos(2*a)+sin(2*a))
cos(pi/(2-3*a))^2-(-cos(3*a))^2
cos(pi/4-a)/(1-sin(2a))^(-1)-(sin(pi/4-a))/(1+sin(2a))^(-1)
cos(4*x)/(cos(2*x)-sin(2*x))
Tangente tan
tan(x)^(sqrt(x))*(log(tan(x))/(2*sqrt(x))+sqrt(x)*(1+tan(x)^2)/tan(x))
tan(x/2)/(x^2+x-2)
tan(x)^2*(3+3*tan(x)^2)/(1+tan(x)^2)-tan(x)^4*(2+2*tan(x)^2)/(1+tan(x)^2)^2
tan(x+pi/8)/2-1/(2*tan(x+pi/8))
tan(pi/8)/(1-tan^2(pi/8))
Raíz cuadrada sqrt
sqrt(x)*cos(x)+sin(x)/(2*sqrt(x))
sqrt(2)*(2+cot(x)^2+tan(x)^2)/(2*(1+(tan(x)-cot(x))^2/2))
sqrt(((a*b*c+4)/a)+4*sqrt(b*c/a))/(sqrt(a*b*c)+2)
sqrt(2)/(sqrt(8)+2)-(6-sqrt(32))/sqrt((8)-3)
sqrt(2)/(sqrt(8)+2)-((6-sqrt(32))/sqrt(8)-3)
Coseno cos
cos((\pi)/(2)+a)cos(\pi-a)+sin((3\pi)/(2)+a)sin(\pi+a)
cos(4*a)/(cos(2*a)+sin(2*a))
cos(pi/(2-3*a))^2-(-cos(3*a))^2
cos(pi/4-a)/(1-sin(2a))^(-1)-(sin(pi/4-a))/(1+sin(2a))^(-1)
cos(4*x)/(cos(2*x)-sin(2*x))
Coseno cos
cos((\pi)/(2)+a)cos(\pi-a)+sin((3\pi)/(2)+a)sin(\pi+a)
cos(4*a)/(cos(2*a)+sin(2*a))
cos(pi/(2-3*a))^2-(-cos(3*a))^2
cos(pi/4-a)/(1-sin(2a))^(-1)-(sin(pi/4-a))/(1+sin(2a))^(-1)
cos(4*x)/(cos(2*x)-sin(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                 /  2            
    pi*a                 /  a  + a*cos(l) 
--------------*tan(f)*  /   ------------- 
6*(1 - cos(l))        \/      4 - cos(l)

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

- \frac{\pi a^{2} \sqrt{- \frac{a \left(a + \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*(a + 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))

Combinatoria [src]

           ________________        
     2    / 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)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}

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

Unión de expresiones racionales [src]

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

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

Potencias [src]

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

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

                  _______________________                 
                 /        / I*l    -I*l\                  
                /   2     |e      e    |                  
               /   a  + a*|---- + -----|                  
      2       /           \ 2       2  /  /   I*f    -I*f\
pi*I*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{\frac{a^{2} + 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)))

Denominador racional [src]

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

\frac{\pi a^{2} \sqrt{\frac{a^{2} + 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))

Denominador común [src]

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

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

Abrimos la expresión [src]

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

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

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

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

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

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

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

Compilar la expresión [src]

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

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

\frac{\pi a^{2} \sqrt{\frac{a^{2} + 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)}}

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

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

                      _______________________
                     /        /        2/l\\ 
                    /       a*|-1 + cot |-|| 
                   /    2     \         \2// 
                  /    a  + ---------------- 
                 /                   2/l\    
                /             1 + cot |-|    
    2          /                      \2/    
pi*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{\frac{a^{2} + \frac{a \left(\cot^{2}{\left(\frac{l}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{l}{2} \right)} + 1}}{- \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        a                  
                /  a  + -----------             
               /           /pi    \             
              /         csc|-- - l|             
    2        /             \2     /     /pi    \
pi*a *      /      ---------------- *csc|-- - f|
           /                1           \2     /
          /        4 - -----------              
         /                /pi    \              
        /              csc|-- - l|              
      \/                  \2     /              
------------------------------------------------
            /         6     \                   
            |6 - -----------|*csc(f)            
            |       /pi    \|                   
            |    csc|-- - l||                   
            \       \2     //

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

\frac{2 \pi a^{2} \sqrt{\frac{a^{2} + 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/l\\         
                     /    |    1 - tan |-||         
                    /     |            \2/|         
                   /    a*|a + -----------|         
                  /       |           2/l\|         
                 /        |    1 + tan |-||         
     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(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)}

                      _____________________       
                     /   /           2/l\\        
                    /    |    1 - tan |-||        
                   /     |            \2/|        
                  /    a*|a + -----------|        
                 /       |           2/l\|        
                /        |    1 + tan |-||        
    2          /         \            \2//        
pi*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{\frac{a \left(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)}}{- \frac{6 \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1} + 6}

           ________________        
     2    / 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)}\right)}{4 - \cos{\left(l \right)}}} \tan{\left(f \right)}}{6 \left(\cos{\left(l \right)} - 1\right)}

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

\frac{\pi a^{2} \sqrt{\frac{a^{2} + 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)}}

                   _____________________             
                  /   /         1     \              
                 /  a*|a + -----------|              
                /     |       /pi    \|              
               /      |    csc|-- - l||              
     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(a + \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)}}

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

\frac{\pi a^{2} \sqrt{\frac{a \left(a + \frac{1}{\sec{\left(l \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    / a*(a + 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)}\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\\ 
                    /    |    -1 + cot |-|| 
                   /     |             \2/| 
                  /    a*|a + ------------| 
                 /       |           2/l\ | 
                /        |    1 + cot |-| | 
    2          /         \            \2/ / 
pi*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{\frac{a \left(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}}}{\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//        
                  /    a  + ---------------        
                 /                   2/l\          
                /             1 + tan |-|          
    2          /                      \2/          
pi*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{\frac{a^{2} + \frac{a \left(1 - \tan^{2}{\left(\frac{l}{2} \right)}\right)}{\tan^{2}{\left(\frac{l}{2} \right)} + 1}}{- \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}

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

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

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

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

\frac{2 \pi a^{2} \sqrt{\frac{a^{2} + 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    / a*(a + cos(l))     /    pi\
pi*a *  /  -------------- *cos|f - --|
      \/     4 - cos(l)       \    2 /
--------------------------------------
        (6 - 6*cos(l))*cos(f)

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

               _____________________         
              /   /       /    pi\\          
             /  a*|a + sin|l + --||          
     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)}\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)}}

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

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

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

\frac{\pi a^{2} \sqrt{\frac{a^{2} + \frac{a}{\sec{\left(l \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)}}

               ________________        
              /   /      1   \         
             /  a*|a + ------|         
     2      /     \    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(a + \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)}}

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

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¿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?