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Simplificación de expresiones/ Descomposición en fracciones simples/ exp(x)/(4*(1+(e^x-3)^2/4))

¿Cómo vas a descomponer esta exp(x)/(4*(1+(e^x-3)^2/4)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
         x       
        e        
-----------------
  /            2\
  |    / x    \ |
  |    \E  - 3/ |
4*|1 + ---------|
  \        4    /
ex4((ex−3)24+1)\frac{e^{x}}{4 \left(\frac{\left(e^{x} - 3\right)^{2}}{4} + 1\right)} 
exp(x)/((4*(1 + (E^x - 3)^2/4)))
Descomposición de una fracción [src] 
exp(x)/(13 - 6*exp(x) + exp(2*x))
exe2x−6ex+13\frac{e^{x}}{e^{2 x} - 6 e^{x} + 13} 
        x       
       e        
----------------
        x    2*x
13 - 6*e  + e
Simplificación general [src] 
       x      
      e       
--------------
             2
    /      x\ 
4 + \-3 + e /
ex(ex−3)2+4\frac{e^{x}}{\left(e^{x} - 3\right)^{2} + 4} 
exp(x)/(4 + (-3 + exp(x))^2)
Compilar la expresión [src] 
       x      
      e       
--------------
             2
    /      x\ 
4 + \-3 + e /
ex(ex−3)2+4\frac{e^{x}}{\left(e^{x} - 3\right)^{2} + 4} 
exp(x)/(4 + (-3 + exp(x))^2)
Denominador común [src] 
        x       
       e        
----------------
        x    2*x
13 - 6*e  + e
exe2x−6ex+13\frac{e^{x}}{e^{2 x} - 6 e^{x} + 13} 
exp(x)/(13 - 6*exp(x) + exp(2*x))
Combinatoria [src] 
        x       
       e        
----------------
        x    2*x
13 - 6*e  + e
exe2x−6ex+13\frac{e^{x}}{e^{2 x} - 6 e^{x} + 13} 
exp(x)/(13 - 6*exp(x) + exp(2*x))
Denominador racional [src] 
        x       
       e        
----------------
        x    2*x
13 - 6*e  + e
exe2x−6ex+13\frac{e^{x}}{e^{2 x} - 6 e^{x} + 13} 
exp(x)/(13 - 6*exp(x) + exp(2*x))
Potencias [src] 
       x      
      e       
--------------
             2
    /      x\ 
4 + \-3 + e /
ex(ex−3)2+4\frac{e^{x}}{\left(e^{x} - 3\right)^{2} + 4} 
exp(x)/(4 + (-3 + exp(x))^2)
Respuesta numérica [src] 
exp(x)/(4.0 + 9.0*(-1 + 0.333333333333333*2.71828182845905^x)^2)
exp(x)/(4.0 + 9.0*(-1 + 0.333333333333333*2.71828182845905^x)^2)
Unión de expresiones racionales [src] 
       x      
      e       
--------------
             2
    /      x\ 
4 + \-3 + e /
ex(ex−3)2+4\frac{e^{x}}{\left(e^{x} - 3\right)^{2} + 4} 
exp(x)/(4 + (-3 + exp(x))^2)
Parte trigonométrica [src] 
       x      
      e       
--------------
             2
    /      x\ 
4 + \-3 + e /
ex(ex−3)2+4\frac{e^{x}}{\left(e^{x} - 3\right)^{2} + 4} 
      cosh(x) + sinh(x)      
-----------------------------
                            2
4 + (-3 + cosh(x) + sinh(x))
sinh⁡(x)+cosh⁡(x)(sinh⁡(x)+cosh⁡(x)−3)2+4\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - 3\right)^{2} + 4} 
       cosh(x) + sinh(x)        
--------------------------------
                               2
    /                        x\ 
4 + \-3 + (cosh(1) + sinh(1)) /
sinh⁡(x)+cosh⁡(x)((sinh⁡(1)+cosh⁡(1))x−3)2+4\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - 3\right)^{2} + 4} 
(cosh(x) + sinh(x))/(4 + (-3 + (cosh(1) + sinh(1))^x)^2)
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