How do you exp(-x)/(1+exp(x))^2 in partial fractions?

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    -x   
   e     
---------
        2
/     x\ 
\1 + e /

$$\frac{e^{- x}}{\left(e^{x} + 1\right)^{2}}$$

exp(-x)/(1 + exp(x))^2

Fraction decomposition [src]

-1/(1 + exp(x)) - 1/(1 + exp(x))^2 + exp(-x)

$$e^{- x} - \frac{1}{e^{x} + 1} - \frac{1}{\left(e^{x} + 1\right)^{2}}$$

    1          1        -x
- ------ - --------- + e  
       x           2      
  1 + e    /     x\       
           \1 + e /

Numerical answer [src]

exp(-x)/(1.0 + exp(x))^2

exp(-x)/(1.0 + exp(x))^2

Common denominator [src]

        1         
------------------
   2*x    x    3*x
2*e    + e  + e

$$\frac{1}{e^{3 x} + 2 e^{2 x} + e^{x}}$$

1/(2*exp(2*x) + exp(x) + exp(3*x))

Trigonometric part [src]

 -(-cosh(x) + sinh(x))  
------------------------
                       2
(1 + cosh(x) + sinh(x))

$$- \frac{\sinh{\left(x \right)} - \cosh{\left(x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$

   -sinh(x) + cosh(x)   
------------------------
                       2
(1 + cosh(x) + sinh(x))

$$\frac{- \sinh{\left(x \right)} + \cosh{\left(x \right)}}{\left(\sinh{\left(x \right)} + \cosh{\left(x \right)} + 1\right)^{2}}$$

(-sinh(x) + cosh(x))/(1 + cosh(x) + sinh(x))^2