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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    x      / x    \ /   x    -x\
   e       \E  + 1/*\- E  - e  /
-------- + ---------------------
 x    -x                  2     
E  - E          / x    -x\      
                \E  - E  /
(−ex−e−x)(ex+1)(ex−e−x)2+exex−e−x\frac{\left(- e^{x} - e^{- x}\right) \left(e^{x} + 1\right)}{\left(e^{x} - e^{- x}\right)^{2}} + \frac{e^{x}}{e^{x} - e^{- x}} 
exp(x)/(E^x - E^(-x)) + ((E^x + 1)*(-E^x - exp(-x)))/(E^x - E^(-x))^2
Descomposición de una fracción [src] 
-1/(-1 + exp(x)) - 1/(-1 + exp(x))^2
−1ex−1−1(ex−1)2- \frac{1}{e^{x} - 1} - \frac{1}{\left(e^{x} - 1\right)^{2}} 
     1          1     
- ------- - ----------
        x            2
  -1 + e    /      x\ 
            \-1 + e /
Simplificación general [src] 
        x      
      -e       
---------------
       x    2*x
1 - 2*e  + e
−exe2x−2ex+1- \frac{e^{x}}{e^{2 x} - 2 e^{x} + 1} 
-exp(x)/(1 - 2*exp(x) + exp(2*x))
Combinatoria [src] 
     x    
   -e     
----------
         2
/      x\ 
\-1 + e /
−ex(ex−1)2- \frac{e^{x}}{\left(e^{x} - 1\right)^{2}} 
-exp(x)/(-1 + exp(x))^2
Denominador común [src] 
        x      
      -e       
---------------
       x    2*x
1 - 2*e  + e
−exe2x−2ex+1- \frac{e^{x}}{e^{2 x} - 2 e^{x} + 1} 
-exp(x)/(1 - 2*exp(x) + exp(2*x))
Respuesta numérica [src] 
exp(x)/(2.71828182845905^x - 2.71828182845905^(-x)) + (1.0 + 2.71828182845905^x)*(-2.71828182845905^x - exp(-x))/(2.71828182845905^x - 2.71828182845905^(-x))^2
exp(x)/(2.71828182845905^x - 2.71828182845905^(-x)) + (1.0 + 2.71828182845905^x)*(-2.71828182845905^x - exp(-x))/(2.71828182845905^x - 2.71828182845905^(-x))^2
Unión de expresiones racionales [src] 
//     x\ /      2*x\   /      2*x\  x\  x
\\1 + e /*\-1 - e   / + \-1 + e   /*e /*e 
------------------------------------------
                          2               
               /      2*x\                
               \-1 + e   /
((ex+1)(−e2x−1)+(e2x−1)ex)ex(e2x−1)2\frac{\left(\left(e^{x} + 1\right) \left(- e^{2 x} - 1\right) + \left(e^{2 x} - 1\right) e^{x}\right) e^{x}}{\left(e^{2 x} - 1\right)^{2}} 
((1 + exp(x))*(-1 - exp(2*x)) + (-1 + exp(2*x))*exp(x))*exp(x)/(-1 + exp(2*x))^2
Denominador racional [src] 
/           2                                             \    
|/      2*x\   3*x   /     x\ /      2*x\ /      2*x\  2*x|  -x
\\-1 + e   / *e    + \1 + e /*\-1 - e   /*\-1 + e   /*e   /*e  
---------------------------------------------------------------
                                     3                         
                          /      2*x\                          
                          \-1 + e   /
((ex+1)(−e2x−1)(e2x−1)e2x+(e2x−1)2e3x)e−x(e2x−1)3\frac{\left(\left(e^{x} + 1\right) \left(- e^{2 x} - 1\right) \left(e^{2 x} - 1\right) e^{2 x} + \left(e^{2 x} - 1\right)^{2} e^{3 x}\right) e^{- x}}{\left(e^{2 x} - 1\right)^{3}} 
((-1 + exp(2*x))^2*exp(3*x) + (1 + exp(x))*(-1 - exp(2*x))*(-1 + exp(2*x))*exp(2*x))*exp(-x)/(-1 + exp(2*x))^3
Parte trigonométrica [src] 
cosh(x) + sinh(x)   (1 + cosh(x) + sinh(x))*cosh(x)
----------------- - -------------------------------
    2*sinh(x)                        2             
                               2*sinh (x)
sinh⁡(x)+cosh⁡(x)2sinh⁡(x)−(sinh⁡(x)+cosh⁡(x)+1)cosh⁡(x)2sinh⁡2(x)\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{2 \sinh{\left(x \right)}} - \frac{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right) \cosh{\left(x \right)}}{2 \sinh^{2}{\left(x \right)}} 
                    x /                   2*x                        x                            \ 
-(cosh(1) + sinh(1)) *\(cosh(1) + sinh(1))    - 2*(cosh(1) + sinh(1)) *sinh(x) + cosh(x) + sinh(x)/ 
----------------------------------------------------------------------------------------------------
                                                                            2                       
                      /                       x\ /                        x\                        
                      \1 + (cosh(1) + sinh(1)) /*\-1 + (cosh(1) + sinh(1)) /
−(sinh⁡(1)+cosh⁡(1))x((sinh⁡(1)+cosh⁡(1))2x−2(sinh⁡(1)+cosh⁡(1))xsinh⁡(x)+sinh⁡(x)+cosh⁡(x))((sinh⁡(1)+cosh⁡(1))x−1)2((sinh⁡(1)+cosh⁡(1))x+1)- \frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} \left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{2 x} - 2 \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} \sinh{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - 1\right)^{2} \left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1\right)} 
-(1 + cosh(x)) 
---------------
         2     
   2*sinh (x)
−cosh⁡(x)+12sinh⁡2(x)- \frac{\cosh{\left(x \right)} + 1}{2 \sinh^{2}{\left(x \right)}} 
                                               /                       x\ /                     x                    \
             cosh(x) + sinh(x)                 \1 + (cosh(1) + sinh(1)) /*\- (cosh(1) + sinh(1))  - cosh(x) + sinh(x)/
-------------------------------------------- + -----------------------------------------------------------------------
                   x                      -x                                                             2            
(cosh(1) + sinh(1))  - (cosh(1) + sinh(1))                 /                   x                      -x\             
                                                           \(cosh(1) + sinh(1))  - (cosh(1) + sinh(1))  /
((sinh⁡(1)+cosh⁡(1))x+1)(−(sinh⁡(1)+cosh⁡(1))x+sinh⁡(x)−cosh⁡(x))((sinh⁡(1)+cosh⁡(1))x−(sinh⁡(1)+cosh⁡(1))−x)2+sinh⁡(x)+cosh⁡(x)(sinh⁡(1)+cosh⁡(1))x−(sinh⁡(1)+cosh⁡(1))−x\frac{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1\right) \left(- \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + \sinh{\left(x \right)} - \cosh{\left(x \right)}\right)}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{- x}\right)^{2}} + \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{- x}} 
(cosh(x) + sinh(x))/((cosh(1) + sinh(1))^x - (cosh(1) + sinh(1))^(-x)) + (1 + (cosh(1) + sinh(1))^x)*(-(cosh(1) + sinh(1))^x - cosh(x) + sinh(x))/((cosh(1) + sinh(1))^x - (cosh(1) + sinh(1))^(-x))^2
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