Sr Examen

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

Ha introducido [src]

   x  
  E   
------
     x
1 - E

$$\frac{e^{x}}{1 - e^{x}}$$

E^x/(1 - E^x)

Descomposición de una fracción [src]

-1 - 1/(-1 + exp(x))

$$-1 - \frac{1}{e^{x} - 1}$$

        1   
-1 - -------
           x
     -1 + e

Denominador común [src]

        1   
-1 - -------
           x
     -1 + e

$$-1 - \frac{1}{e^{x} - 1}$$

-1 - 1/(-1 + exp(x))

Combinatoria [src]

    x  
  -e   
-------
      x
-1 + e

$$- \frac{e^{x}}{e^{x} - 1}$$

-exp(x)/(-1 + exp(x))

Respuesta numérica [src]

2.71828182845905^x/(1.0 - 2.71828182845905^x)

2.71828182845905^x/(1.0 - 2.71828182845905^x)

Parte trigonométrica [src]

                     x  
  (cosh(1) + sinh(1))   
------------------------
                       x
1 - (cosh(1) + sinh(1))

$$\frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x}}{1 - \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x}}$$

                      x  
  -(cosh(1) + sinh(1))   
-------------------------
                        x
-1 + (cosh(1) + sinh(1))

$$- \frac{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x}}{\left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{x} - 1}$$

  cosh(x) + sinh(x)  
---------------------
1 - cosh(x) - sinh(x)

$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{- \sinh{\left(x \right)} - \cosh{\left(x \right)} + 1}$$

-(cosh(x) + sinh(x))  
----------------------
-1 + cosh(x) + sinh(x)

$$- \frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{\sinh{\left(x \right)} + \cosh{\left(x \right)} - 1}$$

-(cosh(x) + sinh(x))/(-1 + cosh(x) + sinh(x))