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

An expression to simplify:

The solution

You have entered [src]
  x   
------
 2    
x  - 1
$$\frac{x}{x^{2} - 1}$$
x/(x^2 - 1)
Fraction decomposition [src]
1/(2*(1 + x)) + 1/(2*(-1 + x))
$$\frac{1}{2 \left(x + 1\right)} + \frac{1}{2 \left(x - 1\right)}$$
    1           1     
--------- + ----------
2*(1 + x)   2*(-1 + x)
Numerical answer [src]
x/(-1.0 + x^2)
x/(-1.0 + x^2)
Combinatorics [src]
       x        
----------------
(1 + x)*(-1 + x)
$$\frac{x}{\left(x - 1\right) \left(x + 1\right)}$$
x/((1 + x)*(-1 + x))