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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/
$$- \frac{e^{2 x}}{\left(e^{x} + 1\right)^{2}} + \frac{e^{x}}{e^{x} + 1}$$ 
exp(x)/(E^x + 1) - exp(2*x)/(E^x + 1)^2
Descomposición de una fracción [src] 
1/(1 + exp(x)) - 1/(1 + exp(x))^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
$$\frac{e^{x}}{e^{2 x} + 2 e^{x} + 1}$$ 
exp(x)/(1 + 2*exp(x) + exp(2*x))
Potencias [src] 
   x         2*x  
  e         e     
------ - ---------
     x           2
1 + e    /     x\ 
         \1 + e /
$$\frac{e^{x}}{e^{x} + 1} - \frac{e^{2 x}}{\left(e^{x} + 1\right)^{2}}$$ 
exp(x)/(1 + exp(x)) - exp(2*x)/(1 + exp(x))^2
Combinatoria [src] 
     x   
    e    
---------
        2
/     x\ 
\1 + e /
$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$ 
exp(x)/(1 + exp(x))^2
Denominador común [src] 
        x      
       e       
---------------
       x    2*x
1 + 2*e  + e
$$\frac{e^{x}}{e^{2 x} + 2 e^{x} + 1}$$ 
exp(x)/(1 + 2*exp(x) + exp(2*x))
Compilar la expresión [src] 
   x         2*x  
  e         e     
------ - ---------
     x           2
1 + e    /     x\ 
         \1 + e /
$$\frac{e^{x}}{e^{x} + 1} - \frac{e^{2 x}}{\left(e^{x} + 1\right)^{2}}$$ 
exp(x)/(1 + exp(x)) - exp(2*x)/(1 + exp(x))^2
Unión de expresiones racionales [src] 
     x   
    e    
---------
        2
/     x\ 
\1 + e /
$$\frac{e^{x}}{\left(e^{x} + 1\right)^{2}}$$ 
exp(x)/(1 + exp(x))^2
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
Parte trigonométrica [src] 
  cosh(x) + sinh(x)      cosh(2*x) + sinh(2*x)  
--------------------- - ------------------------
1 + cosh(x) + sinh(x)                          2
                        (1 + cosh(x) + sinh(x))
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$ 
   cosh(x) + sinh(x)          cosh(2*x) + sinh(2*x)   
------------------------ - ---------------------------
                       x                             2
1 + (cosh(1) + sinh(1))    /                       x\ 
                           \1 + (cosh(1) + sinh(1)) /
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1} - \frac{\sinh{\left(2 x \right)} + \cosh{\left(2 x \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} + 1\right)^{2}}$$ 
   cosh(x) + sinh(x)    
------------------------
                       2
(1 + cosh(x) + sinh(x))
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$ 
   x         2*x  
  e         e     
------ - ---------
     x           2
1 + e    /     x\ 
         \1 + e /
$$\frac{e^{x}}{e^{x} + 1} - \frac{e^{2 x}}{\left(e^{x} + 1\right)^{2}}$$ 
exp(x)/(1 + exp(x)) - exp(2*x)/(1 + exp(x))^2
Denominador racional [src] 
        2                   
/     x\   x   /     x\  2*x
\1 + e / *e  - \1 + e /*e   
----------------------------
                 3          
         /     x\           
         \1 + e /
$$\frac{\left(e^{x} + 1\right)^{2} e^{x} - \left(e^{x} + 1\right) e^{2 x}}{\left(e^{x} + 1\right)^{3}}$$ 
((1 + exp(x))^2*exp(x) - (1 + exp(x))*exp(2*x))/(1 + exp(x))^3
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