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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                                                    _______
                                                   / 1 - x 
    _______                                       /  ----- 
   / 1 - x          /      1         1 - x   \  \/   1 + x 
  /  ----- *(1 + x)*|- --------- - ----------|*e           
\/   1 + x          |  2*(1 + x)            2|             
                    \              2*(1 + x) /             
-----------------------------------------------------------
                           1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12(x+1))e1−xx+11−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right) e^{\sqrt{\frac{1 - x}{x + 1}}}}{1 - x} 
(((sqrt((1 - x)/(1 + x))*(1 + x))*(-1/(2*(1 + x)) - (1 - x)/(2*(1 + x)^2)))*exp(sqrt((1 - x)/(1 + x))))/(1 - x)
Simplificación general [src] 
                 _______
                / 1 - x 
    _______    /  ----- 
   / 1 - x   \/   1 + x 
  /  ----- *e           
\/   1 + x              
------------------------
              2         
        -1 + x
1−xx+1e1−xx+1x2−1\frac{\sqrt{\frac{1 - x}{x + 1}} e^{\sqrt{\frac{1 - x}{x + 1}}}}{x^{2} - 1} 
sqrt((1 - x)/(1 + x))*exp(sqrt((1 - x)/(1 + x)))/(-1 + x^2)
Respuesta numérica [src] 
((1.0 - x)/(1.0 + x))^0.5*(1.0 + x)*(-1/(2.0 + 2.0*x) - 0.5*(1.0 - x)/(1.0 + x)^2)*exp(sqrt((1 - x)/(1 + x)))/(1.0 - x)
((1.0 - x)/(1.0 + x))^0.5*(1.0 + x)*(-1/(2.0 + 2.0*x) - 0.5*(1.0 - x)/(1.0 + x)^2)*exp(sqrt((1 - x)/(1 + x)))/(1.0 - x)
Abrimos la expresión [src] 
                                                    _______          
                                                   /   1      _______
    _______                                       /  ----- *\/ 1 - x 
   /   1            /      1         1 - x   \  \/   1 + x           
  /  ----- *(1 + x)*|- --------- - ----------|*e                     
\/   1 + x          |  2*(1 + x)            2|                       
                    \              2*(1 + x) /                       
---------------------------------------------------------------------
                                _______                              
                              \/ 1 - x
(x+1)(−1−x2(x+1)2−12(x+1))1x+1e1−x1x+11−x\frac{\left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x + 1\right)}\right) \sqrt{\frac{1}{x + 1}} e^{\sqrt{1 - x} \sqrt{\frac{1}{x + 1}}}}{\sqrt{1 - x}} 
sqrt(1/(1 + x))*(1 + x)*(-1/(2*(1 + x)) - (1 - x)/(2*(1 + x)^2))*exp(sqrt(1/(1 + x))*sqrt(1 - x))/sqrt(1 - x)
Combinatoria [src] 
                      _______________
                     /   1       x   
    ____________    /  ----- - ----- 
   / -(-1 + x)    \/   1 + x   1 + x 
  /  ---------- *e                   
\/     1 + x                         
-------------------------------------
           (1 + x)*(-1 + x)
−x−1x+1e−xx+1+1x+1(x−1)(x+1)\frac{\sqrt{- \frac{x - 1}{x + 1}} e^{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}}}{\left(x - 1\right) \left(x + 1\right)} 
sqrt(-(-1 + x)/(1 + x))*exp(sqrt(1/(1 + x) - x/(1 + x)))/((1 + x)*(-1 + x))
Compilar la expresión [src] 
                                                  _______
                                                 / 1 - x 
    _______                                     /  ----- 
   / 1 - x          /     1        1 - x   \  \/   1 + x 
  /  ----- *(1 + x)*|- ------- - ----------|*e           
\/   1 + x          |  2 + 2*x            2|             
                    \            2*(1 + x) /             
---------------------------------------------------------
                          1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)e1−xx+11−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) e^{\sqrt{\frac{1 - x}{x + 1}}}}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))*exp(sqrt((1 - x)/(1 + x)))/(1 - x)
Denominador común [src] 
                         _______________
                        /   1       x   
    _______________    /  ----- - ----- 
   /   1       x     \/   1 + x   1 + x 
  /  ----- - ----- *e                   
\/   1 + x   1 + x                      
----------------------------------------
                      2                 
                -1 + x
−xx+1+1x+1e−xx+1+1x+1x2−1\frac{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}} e^{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}}}{x^{2} - 1} 
sqrt(1/(1 + x) - x/(1 + x))*exp(sqrt(1/(1 + x) - x/(1 + x)))/(-1 + x^2)
Potencias [src] 
                                                _______
                    /              1   x \     / 1 - x 
    _______         |            - - + - |    /  ----- 
   / 1 - x          |     1        2   2 |  \/   1 + x 
  /  ----- *(1 + x)*|- ------- + --------|*e           
\/   1 + x          |  2 + 2*x          2|             
                    \            (1 + x) /             
-------------------------------------------------------
                         1 - x
1−xx+1(x+1)(x2−12(x+1)2−12x+2)e1−xx+11−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(\frac{\frac{x}{2} - \frac{1}{2}}{\left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) e^{\sqrt{\frac{1 - x}{x + 1}}}}{1 - x} 
                                                  _______
                                                 / 1 - x 
    _______                                     /  ----- 
   / 1 - x          /     1        1 - x   \  \/   1 + x 
  /  ----- *(1 + x)*|- ------- - ----------|*e           
\/   1 + x          |  2 + 2*x            2|             
                    \            2*(1 + x) /             
---------------------------------------------------------
                          1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)e1−xx+11−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) e^{\sqrt{\frac{1 - x}{x + 1}}}}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))*exp(sqrt((1 - x)/(1 + x)))/(1 - x)
Denominador racional [src] 
                           _______________                                 _______________                                       _______________
                          /   1       x                                   /   1       x                                         /   1       x   
      _______________    /  ----- - -----             _______________    /  ----- - -----                   _______________    /  ----- - ----- 
     /   1       x     \/   1 + x   1 + x       2    /   1       x     \/   1 + x   1 + x             2    /   1       x     \/   1 + x   1 + x 
2*  /  ----- - ----- *e                    - 2*x *  /  ----- - ----- *e                    + 2*(1 + x) *  /  ----- - ----- *e                   
  \/   1 + x   1 + x                              \/   1 + x   1 + x                                    \/   1 + x   1 + x                      
------------------------------------------------------------------------------------------------------------------------------------------------
                                                          2*(1 + x)*(-1 + x)*(2 + 2*x)
−2x2−xx+1+1x+1e−xx+1+1x+1+2(x+1)2−xx+1+1x+1e−xx+1+1x+1+2−xx+1+1x+1e−xx+1+1x+12(x−1)(x+1)(2x+2)\frac{- 2 x^{2} \sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}} e^{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}} + 2 \left(x + 1\right)^{2} \sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}} e^{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}} + 2 \sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}} e^{\sqrt{- \frac{x}{x + 1} + \frac{1}{x + 1}}}}{2 \left(x - 1\right) \left(x + 1\right) \left(2 x + 2\right)} 
(2*sqrt(1/(1 + x) - x/(1 + x))*exp(sqrt(1/(1 + x) - x/(1 + x))) - 2*x^2*sqrt(1/(1 + x) - x/(1 + x))*exp(sqrt(1/(1 + x) - x/(1 + x))) + 2*(1 + x)^2*sqrt(1/(1 + x) - x/(1 + x))*exp(sqrt(1/(1 + x) - x/(1 + x))))/(2*(1 + x)*(-1 + x)*(2 + 2*x))
Unión de expresiones racionales [src] 
                  _______ 
                 / 1 - x  
     _______    /  -----  
    / 1 - x   \/   1 + x  
-  /  ----- *e            
 \/   1 + x               
--------------------------
     (1 + x)*(1 - x)
−1−xx+1e1−xx+1(1−x)(x+1)- \frac{\sqrt{\frac{1 - x}{x + 1}} e^{\sqrt{\frac{1 - x}{x + 1}}}}{\left(1 - x\right) \left(x + 1\right)} 
-sqrt((1 - x)/(1 + x))*exp(sqrt((1 - x)/(1 + x)))/((1 + x)*(1 - x))
Parte trigonométrica [src] 
    _______                                  /    /    _______\       /    _______\\
   / 1 - x          /     1        1 - x   \ |    |   / 1 - x |       |   / 1 - x ||
  /  ----- *(1 + x)*|- ------- - ----------|*|cosh|  /  ----- | + sinh|  /  ----- ||
\/   1 + x          |  2 + 2*x            2| \    \\/   1 + x /       \\/   1 + x //
                    \            2*(1 + x) /                                        
------------------------------------------------------------------------------------
                                       1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)(sinh⁡(1−xx+1)+cosh⁡(1−xx+1))1−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) \left(\sinh{\left(\sqrt{\frac{1 - x}{x + 1}} \right)} + \cosh{\left(\sqrt{\frac{1 - x}{x + 1}} \right)}\right)}{1 - x} 
     ____________                                  /    /    ____________\       /    ____________\\ 
    / -(-1 + x)           /     1        -1 + x  \ |    |   / -(-1 + x)  |       |   / -(-1 + x)  || 
-  /  ---------- *(1 + x)*|- ------- + ----------|*|cosh|  /  ---------- | + sinh|  /  ---------- || 
 \/     1 + x             |  2 + 2*x            2| \    \\/     1 + x    /       \\/     1 + x    // 
                          \            2*(1 + x) /                                                   
-----------------------------------------------------------------------------------------------------
                                                -1 + x
−−x−1x+1(x+1)(x−12(x+1)2−12x+2)(sinh⁡(−x−1x+1)+cosh⁡(−x−1x+1))x−1- \frac{\sqrt{- \frac{x - 1}{x + 1}} \left(x + 1\right) \left(\frac{x - 1}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) \left(\sinh{\left(\sqrt{- \frac{x - 1}{x + 1}} \right)} + \cosh{\left(\sqrt{- \frac{x - 1}{x + 1}} \right)}\right)}{x - 1} 
    ____________                                /    /    ____________\       /    ____________\\
   / -(-1 + x)           /   1        -1 + x  \ |    |   / -(-1 + x)  |       |   / -(-1 + x)  ||
  /  ---------- *(1 + x)*|------- - ----------|*|cosh|  /  ---------- | + sinh|  /  ---------- ||
\/     1 + x             |2 + 2*x            2| \    \\/     1 + x    /       \\/     1 + x    //
                         \          2*(1 + x) /                                                  
-------------------------------------------------------------------------------------------------
                                              -1 + x
−x−1x+1(x+1)(−x−12(x+1)2+12x+2)(sinh⁡(−x−1x+1)+cosh⁡(−x−1x+1))x−1\frac{\sqrt{- \frac{x - 1}{x + 1}} \left(x + 1\right) \left(- \frac{x - 1}{2 \left(x + 1\right)^{2}} + \frac{1}{2 x + 2}\right) \left(\sinh{\left(\sqrt{- \frac{x - 1}{x + 1}} \right)} + \cosh{\left(\sqrt{- \frac{x - 1}{x + 1}} \right)}\right)}{x - 1} 
                                                  _______
                                                 / 1 - x 
    _______                                     /  ----- 
   / 1 - x          /     1        1 - x   \  \/   1 + x 
  /  ----- *(1 + x)*|- ------- - ----------|*e           
\/   1 + x          |  2 + 2*x            2|             
                    \            2*(1 + x) /             
---------------------------------------------------------
                          1 - x
1−xx+1(x+1)(−1−x2(x+1)2−12x+2)e1−xx+11−x\frac{\sqrt{\frac{1 - x}{x + 1}} \left(x + 1\right) \left(- \frac{1 - x}{2 \left(x + 1\right)^{2}} - \frac{1}{2 x + 2}\right) e^{\sqrt{\frac{1 - x}{x + 1}}}}{1 - x} 
sqrt((1 - x)/(1 + x))*(1 + x)*(-1/(2 + 2*x) - (1 - x)/(2*(1 + x)^2))*exp(sqrt((1 - x)/(1 + x)))/(1 - x)
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