$\frac{1}{x-1} + \frac{1}{x+1}$

$\frac{1}{2}(\frac{1}{x+1} - \frac{1}{x-1})$

$\frac{1}{2}(\frac{1}{x-1} - \frac{1}{x+1})$

$\frac{A}{x-1} + \frac{B}{x+1}$