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¿cómo vas a descomponer esta expresión en fracciones?:
(y/(x*y-x^2)+x/(x*y-y^2))/(x^2+2*x*y+y^2)/(1/x+1/y)
(y/(x*y-x^2)+x/(x*y-y^2))/(((x^2+2*x*y+y^2)/(1/x+1/y)))
y/(y+2)+(1/(4-y^2)-1/(4-4*y+y^2))/2/(y-2)^2
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))
Factorizar el polinomio:
y^3-1/8
y^2+x*y-x^3+2*x^2-x*y^2+2*y^2
-y+a*y
y*x^2+x*z^2+z*y^2-y*z^2-x*y^2-z*x^2
Descomponer al cuadrado:
y^4+8*y^2-1
-y^4+7*y^2-4
y^4-8*y^2+1
y^4+8*y^2+1
Expresiones idénticas
tan(dos *x)^ dos /(sqrt(uno -x^ dos)*asin(x)^ dos)-(cuatro + cuatro *tan(dos *x)^ dos)*tan(dos *x)/asin(x)
tangente de (2 multiplicar por x) al cuadrado dividir por ( raíz cuadrada de (1 menos x al cuadrado ) multiplicar por ar coseno de eno de (x) al cuadrado ) menos (4 más 4 multiplicar por tangente de (2 multiplicar por x) al cuadrado ) multiplicar por tangente de (2 multiplicar por x) dividir por ar coseno de eno de (x)
tangente de (dos multiplicar por x) en el grado dos dividir por ( raíz cuadrada de (uno menos x en el grado dos) multiplicar por ar coseno de eno de (x) en el grado dos) menos (cuatro más cuatro multiplicar por tangente de (dos multiplicar por x) en el grado dos) multiplicar por tangente de (dos multiplicar por x) dividir por ar coseno de eno de (x)
tan(2*x)^2/(√(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x)
tan(2*x)2/(sqrt(1-x2)*asin(x)2)-(4+4*tan(2*x)2)*tan(2*x)/asin(x)
tan2*x2/sqrt1-x2*asinx2-4+4*tan2*x2*tan2*x/asinx
tan(2*x)²/(sqrt(1-x²)*asin(x)²)-(4+4*tan(2*x)²)*tan(2*x)/asin(x)
tan(2*x) en el grado 2/(sqrt(1-x en el grado 2)*asin(x) en el grado 2)-(4+4*tan(2*x) en el grado 2)*tan(2*x)/asin(x)
tan(2x)^2/(sqrt(1-x^2)asin(x)^2)-(4+4tan(2x)^2)tan(2x)/asin(x)
tan(2x)2/(sqrt(1-x2)asin(x)2)-(4+4tan(2x)2)tan(2x)/asin(x)
tan2x2/sqrt1-x2asinx2-4+4tan2x2tan2x/asinx
tan2x^2/sqrt1-x^2asinx^2-4+4tan2x^2tan2x/asinx
tan(2*x)^2 dividir por (sqrt(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x) dividir por asin(x)
Expresiones semejantes
tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)-(4-4*tan(2*x)^2)*tan(2*x)/asin(x)
tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)+(4+4*tan(2*x)^2)*tan(2*x)/asin(x)
tan(2*x)^2/(sqrt(1+x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x)
tan(2*x)^2/(sqrt(1-x^2)*arcsin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/arcsin(x)
tan(2*x)^2/(sqrt(1-x^2)*arcsinx^2)-(4+4*tan(2*x)^2)*tan(2*x)/arcsinx
Expresiones con funciones
Tangente tan
tan(2*x)/(tan(4*x)-tan(2*x))
tan(2*a)/(tan(4*a)-tan(2)*a)
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)
tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x))
Raíz cuadrada sqrt
sqrt(x*x-2*x-1)/2-(1+(x-1)/(x-1))/(x-1+(sqrt(x-1))^2-2)+(-1+x)*(x/2-1/2)/sqrt(x*x-2*x-1)
sqrt(x)+(x-3)/(2*sqrt(x))
sqrt((x/(x+1))^2)*(x+1)*(2/(x+1)-2*x/(x+1)^2)/(2*x)
sqrt(x^3/(x-3))*(x-3)*(-x^3/(2*(x-3)^2)+3*x^2/(2*(x-3)))/x^3
sqrt(x)*(5/x+3*sqrt(x)/2)+(5*log(x)+x^(3/2))/(2*sqrt(x))
Tangente tan
tan(2*x)/(tan(4*x)-tan(2*x))
tan(2*a)/(tan(4*a)-tan(2)*a)
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)
tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x))
Tangente tan
tan(2*x)/(tan(4*x)-tan(2*x))
tan(2*a)/(tan(4*a)-tan(2)*a)
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)
tan(2*x)^4*(10+10*tan(2*x)^2)+15*cos(5*x)/(1+3*sin(5*x))

Simplificación de expresiones/ Descomposición en fracciones simples/ tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x)

¿Cómo vas a descomponer esta tan(2x)^2/(sqrt(1-x^2)asin(x)^2)-(4+4tan(2x)^2)tan(2x)/asin(x) expresión en fracciones?

Solución

Ha introducido [src]

        2              /         2     \         
     tan (2*x)         \4 + 4*tan (2*x)/*tan(2*x)
-------------------- - --------------------------
   ________                     asin(x)          
  /      2      2                                
\/  1 - x  *asin (x)

- \frac{\left(4 \tan^{2}{\left(2 x \right)} + 4\right) \tan{\left(2 x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

tan(2*x)^2/((sqrt(1 - x^2)*asin(x)^2)) - (4 + 4*tan(2*x)^2)*tan(2*x)/asin(x)

Simplificación general [src]

        2                               
     tan (2*x)             4*tan(2*x)   
-------------------- - -----------------
   ________                       2     
  /      2      2      asin(x)*cos (2*x)
\/  1 - x  *asin (x)

- \frac{4 \tan{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

tan(2*x)^2/(sqrt(1 - x^2)*asin(x)^2) - 4*tan(2*x)/(asin(x)*cos(2*x)^2)

Combinatoria [src]

 /                 ________                ________                  \          
 |                /      2                /      2     2             |          
-\-tan(2*x) + 4*\/  1 - x  *asin(x) + 4*\/  1 - x  *tan (2*x)*asin(x)/*tan(2*x) 
--------------------------------------------------------------------------------
                           ___________________     2                            
                         \/ -(1 + x)*(-1 + x) *asin (x)

- \frac{\left(4 \sqrt{1 - x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)} + 4 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - \tan{\left(2 x \right)}\right) \tan{\left(2 x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \operatorname{asin}^{2}{\left(x \right)}}

-(-tan(2*x) + 4*sqrt(1 - x^2)*asin(x) + 4*sqrt(1 - x^2)*tan(2*x)^2*asin(x))*tan(2*x)/(sqrt(-(1 + x)*(-1 + x))*asin(x)^2)

Denominador racional [src]

                                                ________                                                                     
      2       3              2                 /      2     2                   2     2       3           2     2            
4*asin (x)*tan (2*x) + 4*asin (x)*tan(2*x) - \/  1 - x  *tan (2*x)*asin(x) - 4*x *asin (x)*tan (2*x) - 4*x *asin (x)*tan(2*x)
-----------------------------------------------------------------------------------------------------------------------------
                                                      /      2\     3                                                        
                                                      \-1 + x /*asin (x)

\frac{- 4 x^{2} \tan^{3}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)} - 4 x^{2} \tan{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)} - \sqrt{1 - x^{2}} \tan^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)} + 4 \tan^{3}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)} + 4 \tan{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{3}{\left(x \right)}}

(4*asin(x)^2*tan(2*x)^3 + 4*asin(x)^2*tan(2*x) - sqrt(1 - x^2)*tan(2*x)^2*asin(x) - 4*x^2*asin(x)^2*tan(2*x)^3 - 4*x^2*asin(x)^2*tan(2*x))/((-1 + x^2)*asin(x)^3)

Denominador común [src]

 /                   ________                          ________                 \ 
 |     2            /      2     3                    /      2                  | 
-\- tan (2*x) + 4*\/  1 - x  *tan (2*x)*asin(x) + 4*\/  1 - x  *asin(x)*tan(2*x)/ 
----------------------------------------------------------------------------------
                                  ________                                        
                                 /      2      2                                  
                               \/  1 - x  *asin (x)

- \frac{4 \sqrt{1 - x^{2}} \tan^{3}{\left(2 x \right)} \operatorname{asin}{\left(x \right)} + 4 \sqrt{1 - x^{2}} \tan{\left(2 x \right)} \operatorname{asin}{\left(x \right)} - \tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

-(-tan(2*x)^2 + 4*sqrt(1 - x^2)*tan(2*x)^3*asin(x) + 4*sqrt(1 - x^2)*asin(x)*tan(2*x))/(sqrt(1 - x^2)*asin(x)^2)

Potencias [src]

                                               /                          2\                     
                                               |      /   2*I*x    -2*I*x\ |                     
                                               |    4*\- e      + e      / | /   2*I*x    -2*I*x\
                                             I*|4 - -----------------------|*\- e      + e      /
                               2               |                        2  |                     
           /   2*I*x    -2*I*x\                |      / -2*I*x    2*I*x\   |                     
           \- e      + e      /                \      \e       + e     /   /                     
- ---------------------------------------- - ----------------------------------------------------
     ________                   2                         / -2*I*x    2*I*x\                     
    /      2  / -2*I*x    2*I*x\      2                   \e       + e     /*asin(x)             
  \/  1 - x  *\e       + e     / *asin (x)

- \frac{i \left(- \frac{4 \left(- e^{2 i x} + e^{- 2 i x}\right)^{2}}{\left(e^{2 i x} + e^{- 2 i x}\right)^{2}} + 4\right) \left(- e^{2 i x} + e^{- 2 i x}\right)}{\left(e^{2 i x} + e^{- 2 i x}\right) \operatorname{asin}{\left(x \right)}} - \frac{\left(- e^{2 i x} + e^{- 2 i x}\right)^{2}}{\sqrt{1 - x^{2}} \left(e^{2 i x} + e^{- 2 i x}\right)^{2} \operatorname{asin}^{2}{\left(x \right)}}

-(-exp(2*i*x) + exp(-2*i*x))^2/(sqrt(1 - x^2)*(exp(-2*i*x) + exp(2*i*x))^2*asin(x)^2) - i*(4 - 4*(-exp(2*i*x) + exp(-2*i*x))^2/(exp(-2*i*x) + exp(2*i*x))^2)*(-exp(2*i*x) + exp(-2*i*x))/((exp(-2*i*x) + exp(2*i*x))*asin(x))

Unión de expresiones racionales [src]

/       ________                                   \         
|      /      2  /       2     \                   |         
\- 4*\/  1 - x  *\1 + tan (2*x)/*asin(x) + tan(2*x)/*tan(2*x)
-------------------------------------------------------------
                        ________                             
                       /      2      2                       
                     \/  1 - x  *asin (x)

\frac{\left(- 4 \sqrt{1 - x^{2}} \left(\tan^{2}{\left(2 x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + \tan{\left(2 x \right)}\right) \tan{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

(-4*sqrt(1 - x^2)*(1 + tan(2*x)^2)*asin(x) + tan(2*x))*tan(2*x)/(sqrt(1 - x^2)*asin(x)^2)

Abrimos la expresión [src]

                                     3                                                                                                          2                                         
                               32*tan (x)                                         8*tan(x)                                                 4*tan (x)                                      
- ------------------------------------------------------------------- - --------------------------- + ------------------------------------------------------------------------------------
       6                   2                   4                             2                           ________               ________                         ________                 
  - tan (x)*asin(x) - 3*tan (x)*asin(x) + 3*tan (x)*asin(x) + asin(x)   - tan (x)*asin(x) + asin(x)     /      2      2        /      2      2       4          /      2      2       2   
                                                                                                      \/  1 - x  *asin (x) + \/  1 - x  *asin (x)*tan (x) - 2*\/  1 - x  *asin (x)*tan (x)

- \frac{32 \tan^{3}{\left(x \right)}}{- \tan^{6}{\left(x \right)} \operatorname{asin}{\left(x \right)} + 3 \tan^{4}{\left(x \right)} \operatorname{asin}{\left(x \right)} - 3 \tan^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)} + \operatorname{asin}{\left(x \right)}} + \frac{4 \tan^{2}{\left(x \right)}}{\sqrt{1 - x^{2}} \tan^{4}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} - 2 \sqrt{1 - x^{2}} \tan^{2}{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} + \sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{8 \tan{\left(x \right)}}{- \tan^{2}{\left(x \right)} \operatorname{asin}{\left(x \right)} + \operatorname{asin}{\left(x \right)}}

-32*tan(x)^3/(-tan(x)^6*asin(x) - 3*tan(x)^2*asin(x) + 3*tan(x)^4*asin(x) + asin(x)) - 8*tan(x)/(-tan(x)^2*asin(x) + asin(x)) + 4*tan(x)^2/(sqrt(1 - x^2)*asin(x)^2 + sqrt(1 - x^2)*asin(x)^2*tan(x)^4 - 2*sqrt(1 - x^2)*asin(x)^2*tan(x)^2)

Respuesta numérica [src]

(1.0 - x^2)^(-0.5)*tan(2*x)^2/asin(x)^2 - (4.0 + 4.0*tan(2*x)^2)*tan(2*x)/asin(x)

(1.0 - x^2)^(-0.5)*tan(2*x)^2/asin(x)^2 - (4.0 + 4.0*tan(2*x)^2)*tan(2*x)/asin(x)

Parte trigonométrica [src]

        2                   3              
     tan (2*x)         4*sec (2*x)*sin(2*x)
-------------------- - --------------------
   ________                  asin(x)       
  /      2      2                          
\/  1 - x  *asin (x)

- \frac{4 \sin{\left(2 x \right)} \sec^{3}{\left(2 x \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

   2               1                 4*tan(2*x)   
tan (2*x)*-------------------- - -----------------
             ________                       2     
            /      2      2      asin(x)*cos (2*x)
          \/  1 - x  *asin (x)

\frac{1}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} \tan^{2}{\left(2 x \right)} - \frac{4 \tan{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}}

        /      pi\               2/      pi\        
   4*cos|2*x - --|            cos |2*x - --|        
        \      2 /                \      2 /        
- ----------------- + ------------------------------
             3           ________                   
  asin(x)*cos (2*x)     /      2      2       2     
                      \/  1 - x  *asin (x)*cos (2*x)

- \frac{4 \cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{3}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

        2                               
     tan (2*x)             4*tan(2*x)   
-------------------- - -----------------
   ________                       2     
  /      2      2      asin(x)*cos (2*x)
\/  1 - x  *asin (x)

- \frac{4 \tan{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

                                    4               
      4*sin(2*x)               4*sin (2*x)          
- ----------------- + ------------------------------
             3           ________                   
  asin(x)*cos (2*x)     /      2      2       2     
                      \/  1 - x  *asin (x)*sin (4*x)

- \frac{4 \sin{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                 2                                4               
            8*sin (2*x)                      4*sin (2*x)          
- ------------------------------- + ------------------------------
                      2/pi      \      ________                   
  asin(x)*sin(4*x)*sin |-- + 2*x|     /      2      2       2     
                       \2       /   \/  1 - x  *asin (x)*sin (4*x)

- \frac{8 \sin^{2}{\left(2 x \right)}}{\sin{\left(4 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{2} \right)} \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                                                         2                 
                                                                          /       2     \     4            
                          32*cot(x)                                    16*\1 + cot (2*x)/ *cot (x)         
- --------------------------------------------------------- + ---------------------------------------------
                /        2          /        2   \\                        4    ________                   
  /       2   \ |-1 + cot (3*x)   3*\-1 + cot (x)/|           /       2   \    /      2      2       2     
  \1 + cot (x)/*|-------------- + ----------------|*asin(x)   \1 + cot (x)/ *\/  1 - x  *asin (x)*cot (2*x)
                |       2                  2      |                                                        
                \1 + cot (3*x)      1 + cot (x)   /

- \frac{32 \cot{\left(x \right)}}{\left(\frac{3 \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1} + \frac{\cot^{2}{\left(3 x \right)} - 1}{\cot^{2}{\left(3 x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}} + \frac{16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \cot^{4}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(\cot^{2}{\left(x \right)} + 1\right)^{4} \cot^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                  2               
            16*sin(2*x)                      4*csc (4*x)          
- ------------------------------- + ------------------------------
  (3*cos(2*x) + cos(6*x))*asin(x)      ________                   
                                      /      2      2       4     
                                    \/  1 - x  *asin (x)*csc (2*x)

- \frac{16 \sin{\left(2 x \right)}}{\left(3 \cos{\left(2 x \right)} + \cos{\left(6 x \right)}\right) \operatorname{asin}{\left(x \right)}} + \frac{4 \csc^{2}{\left(4 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \csc^{4}{\left(2 x \right)}}

                                      2         
        2                /       2   \          
     tan (2*x)         4*\1 + tan (x)/ *tan(2*x)
-------------------- - -------------------------
   ________                           2         
  /      2      2        /       2   \          
\/  1 - x  *asin (x)     \1 - tan (x)/ *asin(x)

- \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(2 x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

        2                                            
     tan (2*x)                    8*tan(x)           
-------------------- - ------------------------------
   ________                         3                
  /      2      2      /       2   \             4   
\/  1 - x  *asin (x)   \1 - tan (x)/ *asin(x)*cos (x)

- \frac{8 \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{3} \cos^{4}{\left(x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

        2                                             
     tan (2*x)                     8*cot(x)           
-------------------- - -------------------------------
   ________                          3                
  /      2      2      /        2   \             4   
\/  1 - x  *asin (x)   \-1 + cot (x)/ *asin(x)*sin (x)

- \frac{8 \cot{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{3} \sin^{4}{\left(x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

         2                         4               
    8*tan (2*x)               4*sin (2*x)          
- ---------------- + ------------------------------
  asin(x)*sin(4*x)      ________                   
                       /      2      2       2     
                     \/  1 - x  *asin (x)*sin (4*x)

- \frac{8 \tan^{2}{\left(2 x \right)}}{\sin{\left(4 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                                                       2                 
                                                                        /       2     \     4            
                         32*tan(x)                                   16*\1 + tan (2*x)/ *tan (x)         
- ------------------------------------------------------- + ---------------------------------------------
                /       2          /       2   \\                        4    ________                   
  /       2   \ |1 - tan (3*x)   3*\1 - tan (x)/|           /       2   \    /      2      2       2     
  \1 + tan (x)/*|------------- + ---------------|*asin(x)   \1 + tan (x)/ *\/  1 - x  *asin (x)*tan (2*x)
                |       2                 2     |                                                        
                \1 + tan (3*x)     1 + tan (x)  /

- \frac{32 \tan{\left(x \right)}}{\left(\frac{3 \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1} + \frac{1 - \tan^{2}{\left(3 x \right)}}{\tan^{2}{\left(3 x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}} + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \tan^{4}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(\tan^{2}{\left(x \right)} + 1\right)^{4} \tan^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

       3/pi      \              2/pi      \        
  4*csc |-- - 2*x|           csc |-- - 2*x|        
        \2       /               \2       /        
- ---------------- + ------------------------------
  asin(x)*csc(2*x)      ________                   
                       /      2      2       2     
                     \/  1 - x  *asin (x)*csc (2*x)

- \frac{4 \csc^{3}{\left(- 2 x + \frac{\pi}{2} \right)}}{\operatorname{asin}{\left(x \right)} \csc{\left(2 x \right)}} + \frac{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \csc^{2}{\left(2 x \right)}}

            3                             2                  
       4*sec (2*x)                     sec (2*x)             
- --------------------- + -----------------------------------
             /      pi\      ________                        
  asin(x)*sec|2*x - --|     /      2      2       2/      pi\
             \      2 /   \/  1 - x  *asin (x)*sec |2*x - --|
                                                   \      2 /

- \frac{4 \sec^{3}{\left(2 x \right)}}{\operatorname{asin}{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}

                                                  4               
            16*sin(2*x)                      4*sin (2*x)          
- ------------------------------- + ------------------------------
  (3*cos(2*x) + cos(6*x))*asin(x)      ________                   
                                      /      2      2       2     
                                    \/  1 - x  *asin (x)*sin (4*x)

- \frac{16 \sin{\left(2 x \right)}}{\left(3 \cos{\left(2 x \right)} + \cos{\left(6 x \right)}\right) \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                        2        
                                           /       2   \         
              1                          4*\1 + cot (x)/         
------------------------------ - --------------------------------
   ________                                    2                 
  /      2      2       2        /        2   \                  
\/  1 - x  *asin (x)*cot (2*x)   \-1 + cot (x)/ *asin(x)*cot(2*x)

- \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{2} \cot{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{1}{\sqrt{1 - x^{2}} \cot^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                                   2               
                         16                                   4*csc (4*x)          
- ------------------------------------------------ + ------------------------------
  /      1               3      \                       ________                   
  |------------- + -------------|*asin(x)*csc(2*x)     /      2      2       4     
  |   /pi      \      /pi      \|                    \/  1 - x  *asin (x)*csc (2*x)
  |csc|-- - 6*x|   csc|-- - 2*x||                                                  
  \   \2       /      \2       //

- \frac{16}{\left(\frac{3}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 6 x + \frac{\pi}{2} \right)}}\right) \operatorname{asin}{\left(x \right)} \csc{\left(2 x \right)}} + \frac{4 \csc^{2}{\left(4 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \csc^{4}{\left(2 x \right)}}

                                 /         2/      pi\\              
                                 |    4*cos |2*x - --||              
                                 |          \      2 /|    /      pi\
           2/      pi\           |4 + ----------------|*cos|2*x - --|
        cos |2*x - --|           |          2         |    \      2 /
            \      2 /           \       cos (2*x)    /              
------------------------------ - ------------------------------------
   ________                                asin(x)*cos(2*x)          
  /      2      2       2                                            
\/  1 - x  *asin (x)*cos (2*x)

- \frac{\left(4 + \frac{4 \cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 x \right)}}\right) \cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\cos^{2}{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

            16*sin(2*x)                         1 - cos(4*x)           
- ------------------------------- + -----------------------------------
  (3*cos(2*x) + cos(6*x))*asin(x)      ________                        
                                      /      2                     2   
                                    \/  1 - x  *(1 + cos(4*x))*asin (x)

- \frac{16 \sin{\left(2 x \right)}}{\left(3 \cos{\left(2 x \right)} + \cos{\left(6 x \right)}\right) \operatorname{asin}{\left(x \right)}} + \frac{1 - \cos{\left(4 x \right)}}{\sqrt{1 - x^{2}} \left(\cos{\left(4 x \right)} + 1\right) \operatorname{asin}^{2}{\left(x \right)}}

        2                                             
     tan (2*x)                    4*tan(2*x)          
-------------------- - -------------------------------
   ________                          2                
  /      2      2      /        2   \             4   
\/  1 - x  *asin (x)   \-1 + cot (x)/ *asin(x)*sin (x)

- \frac{4 \tan{\left(2 x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{2} \sin^{4}{\left(x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

                /      pi\                         4/      pi\         
          16*cos|2*x - --|                    4*cos |2*x - --|         
                \      2 /                          \      2 /         
- ------------------------------- + -----------------------------------
  (3*cos(2*x) + cos(6*x))*asin(x)      ________                        
                                      /      2      2       2/      pi\
                                    \/  1 - x  *asin (x)*cos |4*x - --|
                                                             \      2 /

- \frac{16 \cos{\left(2 x - \frac{\pi}{2} \right)}}{\left(3 \cos{\left(2 x \right)} + \cos{\left(6 x \right)}\right) \operatorname{asin}{\left(x \right)}} + \frac{4 \cos^{4}{\left(2 x - \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(4 x - \frac{\pi}{2} \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                                            4               
                 16*sin(2*x)                           4*sin (2*x)          
- ----------------------------------------- + ------------------------------
  /     /pi      \      /pi      \\              ________                   
  |3*sin|-- + 2*x| + sin|-- + 6*x||*asin(x)     /      2      2       2     
  \     \2       /      \2       //           \/  1 - x  *asin (x)*sin (4*x)

- \frac{16 \sin{\left(2 x \right)}}{\left(3 \sin{\left(2 x + \frac{\pi}{2} \right)} + \sin{\left(6 x + \frac{\pi}{2} \right)}\right) \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

        2                                 
     tan (2*x)         4*sec(2*x)*sin(2*x)
-------------------- - -------------------
   ________                        2      
  /      2      2       asin(x)*cos (2*x) 
\/  1 - x  *asin (x)

- \frac{4 \sin{\left(2 x \right)} \sec{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

                                      /          2       \         
                                      |     4*sec (2*x)  |         
                                      |4 + --------------|*sec(2*x)
                                      |       2/      pi\|         
                2                     |    sec |2*x - --||         
             sec (2*x)                \        \      2 //         
----------------------------------- - -----------------------------
   ________                                          /      pi\    
  /      2      2       2/      pi\       asin(x)*sec|2*x - --|    
\/  1 - x  *asin (x)*sec |2*x - --|                  \      2 /    
                         \      2 /

- \frac{\left(\frac{4 \sec^{2}{\left(2 x \right)}}{\sec^{2}{\left(2 x - \frac{\pi}{2} \right)}} + 4\right) \sec{\left(2 x \right)}}{\operatorname{asin}{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \sec^{2}{\left(2 x - \frac{\pi}{2} \right)}}

                                      2       
        2                /       2   \        
     tan (2*x)         8*\1 + tan (x)/ *tan(x)
-------------------- - -----------------------
   ________                          3        
  /      2      2       /       2   \         
\/  1 - x  *asin (x)    \1 - tan (x)/ *asin(x)

- \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{3} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

                                                               2/      pi\         
                                                          4*sec |4*x - --|         
                       16                                       \      2 /         
- ------------------------------------------- + -----------------------------------
  /   1          3    \            /      pi\      ________                        
  |-------- + --------|*asin(x)*sec|2*x - --|     /      2      2       4/      pi\
  \sec(6*x)   sec(2*x)/            \      2 /   \/  1 - x  *asin (x)*sec |2*x - --|
                                                                         \      2 /

- \frac{16}{\left(\frac{1}{\sec{\left(6 x \right)}} + \frac{3}{\sec{\left(2 x \right)}}\right) \operatorname{asin}{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{4 \sec^{2}{\left(4 x - \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \sec^{4}{\left(2 x - \frac{\pi}{2} \right)}}

                                 /         2     \         
                                 |    4*sin (2*x)|         
                                 |4 + -----------|*sin(2*x)
             2                   |        2      |         
          sin (2*x)              \     cos (2*x) /         
------------------------------ - --------------------------
   ________                           asin(x)*cos(2*x)     
  /      2      2       2                                  
\/  1 - x  *asin (x)*cos (2*x)

- \frac{\left(\frac{4 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + 4\right) \sin{\left(2 x \right)}}{\cos{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\sin^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \cos^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                 /         2     \         
                                 |    4*sec (2*x)|         
                                 |4 + -----------|*sec(2*x)
             2                   |        2      |         
          sec (2*x)              \     csc (2*x) /         
------------------------------ - --------------------------
   ________                           asin(x)*csc(2*x)     
  /      2      2       2                                  
\/  1 - x  *asin (x)*csc (2*x)

- \frac{\left(4 + \frac{4 \sec^{2}{\left(2 x \right)}}{\csc^{2}{\left(2 x \right)}}\right) \sec{\left(2 x \right)}}{\operatorname{asin}{\left(x \right)} \csc{\left(2 x \right)}} + \frac{\sec^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \csc^{2}{\left(2 x \right)}}

                                          4      
                                  4 + ---------  
                                         2       
              1                       cot (2*x)  
------------------------------ - ----------------
   ________                      asin(x)*cot(2*x)
  /      2      2       2                        
\/  1 - x  *asin (x)*cot (2*x)

- \frac{4 + \frac{4}{\cot^{2}{\left(2 x \right)}}}{\cot{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{1}{\sqrt{1 - x^{2}} \cot^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

              /          4     \                                 
       2      |    16*sin (2*x)|                                 
  2*sin (2*x)*|4 + ------------|                                 
              |        2       |                 4               
              \     sin (4*x)  /            4*sin (2*x)          
- ------------------------------ + ------------------------------
         asin(x)*sin(4*x)             ________                   
                                     /      2      2       2     
                                   \/  1 - x  *asin (x)*sin (4*x)

- \frac{2 \left(\frac{16 \sin^{4}{\left(2 x \right)}}{\sin^{2}{\left(4 x \right)}} + 4\right) \sin^{2}{\left(2 x \right)}}{\sin{\left(4 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                         4               
        4*sin(2*x)                  4*sin (2*x)          
- ---------------------- + ------------------------------
             3/pi      \      ________                   
  asin(x)*sin |-- + 2*x|     /      2      2       2     
              \2       /   \/  1 - x  *asin (x)*sin (4*x)

- \frac{4 \sin{\left(2 x \right)}}{\sin^{3}{\left(2 x + \frac{\pi}{2} \right)} \operatorname{asin}{\left(x \right)}} + \frac{4 \sin^{4}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

        2                                            
     tan (2*x)                   4*tan(2*x)          
-------------------- - ------------------------------
   ________                         2                
  /      2      2      /       2   \             4   
\/  1 - x  *asin (x)   \1 - tan (x)/ *asin(x)*cos (x)

- \frac{4 \tan{\left(2 x \right)}}{\left(1 - \tan^{2}{\left(x \right)}\right)^{2} \cos^{4}{\left(x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

                                                2       
                                   /       2   \        
              1                  8*\1 + cot (x)/ *cot(x)
------------------------------ - -----------------------
   ________                                    3        
  /      2      2       2        /        2   \         
\/  1 - x  *asin (x)*cot (2*x)   \-1 + cot (x)/ *asin(x)

- \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(\cot^{2}{\left(x \right)} - 1\right)^{3} \operatorname{asin}{\left(x \right)}} + \frac{1}{\sqrt{1 - x^{2}} \cot^{2}{\left(2 x \right)} \operatorname{asin}^{2}{\left(x \right)}}

                                 /         2/pi      \\              
                                 |    4*csc |-- - 2*x||              
                                 |          \2       /|    /pi      \
           2/pi      \           |4 + ----------------|*csc|-- - 2*x|
        csc |-- - 2*x|           |          2         |    \2       /
            \2       /           \       csc (2*x)    /              
------------------------------ - ------------------------------------
   ________                                asin(x)*csc(2*x)          
  /      2      2       2                                            
\/  1 - x  *asin (x)*csc (2*x)

- \frac{\left(4 + \frac{4 \csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 x \right)}}\right) \csc{\left(- 2 x + \frac{\pi}{2} \right)}}{\operatorname{asin}{\left(x \right)} \csc{\left(2 x \right)}} + \frac{\csc^{2}{\left(- 2 x + \frac{\pi}{2} \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} \csc^{2}{\left(2 x \right)}}

        2                               
     tan (2*x)             4*sin(2*x)   
-------------------- - -----------------
   ________                       3     
  /      2      2      asin(x)*cos (2*x)
\/  1 - x  *asin (x)

- \frac{4 \sin{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)} \operatorname{asin}{\left(x \right)}} + \frac{\tan^{2}{\left(2 x \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}}

tan(2*x)^2/(sqrt(1 - x^2)*asin(x)^2) - 4*sin(2*x)/(asin(x)*cos(2*x)^3)

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¿Cómo vas a descomponer esta tan(2*x)^2/(sqrt(1-x^2)*asin(x)^2)-(4+4*tan(2*x)^2)*tan(2*x)/asin(x) expresión en fracciones?

Solución

¿Cómo vas a descomponer esta tan(2x)^2/(sqrt(1-x^2)asin(x)^2)-(4+4tan(2x)^2)tan(2x)/asin(x) expresión en fracciones?