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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   x         2*x  
  e         e     
------ - ---------
 x               2
E  - 1   / x    \ 
         \E  - 1/
−e2x(ex−1)2+exex−1- \frac{e^{2 x}}{\left(e^{x} - 1\right)^{2}} + \frac{e^{x}}{e^{x} - 1} 
exp(x)/(E^x - 1) - exp(2*x)/(E^x - 1)^2
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))
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 /
Respuesta numérica [src] 
exp(x)/(-1.0 + 2.71828182845905^x) - exp(2*x)/(-1.0 + 2.71828182845905^x)^2
exp(x)/(-1.0 + 2.71828182845905^x) - exp(2*x)/(-1.0 + 2.71828182845905^x)^2
Denominador racional [src] 
         2                    
/      x\   x   /      x\  2*x
\-1 + e / *e  - \-1 + e /*e   
------------------------------
                   3          
          /      x\           
          \-1 + e /
(ex−1)2ex−(ex−1)e2x(ex−1)3\frac{\left(e^{x} - 1\right)^{2} e^{x} - \left(e^{x} - 1\right) e^{2 x}}{\left(e^{x} - 1\right)^{3}} 
((-1 + exp(x))^2*exp(x) - (-1 + exp(x))*exp(2*x))/(-1 + exp(x))^3
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
Compilar la expresión [src] 
    x         2*x   
   e         e      
------- - ----------
      x            2
-1 + e    /      x\ 
          \-1 + e /
exex−1−e2x(ex−1)2\frac{e^{x}}{e^{x} - 1} - \frac{e^{2 x}}{\left(e^{x} - 1\right)^{2}} 
exp(x)/(-1 + exp(x)) - exp(2*x)/(-1 + exp(x))^2
Potencias [src] 
    x         2*x   
   e         e      
------- - ----------
      x            2
-1 + e    /      x\ 
          \-1 + e /
exex−1−e2x(ex−1)2\frac{e^{x}}{e^{x} - 1} - \frac{e^{2 x}}{\left(e^{x} - 1\right)^{2}} 
exp(x)/(-1 + exp(x)) - exp(2*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))
Parte trigonométrica [src] 
    x         2*x   
   e         e      
------- - ----------
      x            2
-1 + e    /      x\ 
          \-1 + e /
exex−1−e2x(ex−1)2\frac{e^{x}}{e^{x} - 1} - \frac{e^{2 x}}{\left(e^{x} - 1\right)^{2}} 
    cosh(x) + sinh(x)          cosh(2*x) + sinh(2*x)    
------------------------- - ----------------------------
                        x                              2
-1 + (cosh(1) + sinh(1))    /                        x\ 
                            \-1 + (cosh(1) + sinh(1)) /
sinh⁡(x)+cosh⁡(x)(sinh⁡(1)+cosh⁡(1))x−1−sinh⁡(2x)+cosh⁡(2x)((sinh⁡(1)+cosh⁡(1))x−1)2\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - 1} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - 1\right)^{2}} 
  -(cosh(x) + sinh(x))   
-------------------------
                        2
(-1 + cosh(x) + sinh(x))
−sinh⁡(x)+cosh⁡(x)(sinh⁡(x)+cosh⁡(x)−1)2- \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - 1\right)^{2}} 
  cosh(x) + sinh(x)        cosh(2*x) + sinh(2*x)  
---------------------- - -------------------------
-1 + cosh(x) + sinh(x)                           2
                         (-1 + cosh(x) + sinh(x))
sinh⁡(x)+cosh⁡(x)sinh⁡(x)+cosh⁡(x)−1−sinh⁡(2x)+cosh⁡(2x)(sinh⁡(x)+cosh⁡(x)−1)2\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sinh{\left(x \right)} + \cosh{\left(x \right)} - 1} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - 1\right)^{2}} 
(cosh(x) + sinh(x))/(-1 + cosh(x) + sinh(x)) - (cosh(2*x) + sinh(2*x))/(-1 + cosh(x) + sinh(x))^2
Unión de expresiones racionales [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
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