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

An expression to simplify:

The solution

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