Answer
$\frac{2x}{(x-1)(x+1)}$
Work Step by Step
$\frac{1}{x+1}+\frac{1}{x-1}$
Find the lowest common denominator (i.e. $(x+1)(x-1)$) and adjust the fractions accordingly:
$=\frac{1\times (x-1)}{(x-1)(x+1)}+\frac{1\times (x+1)}{(x-1)(x+1)}$
Expand any brackets:
$=\frac{x-1}{(x-1)(x+1)}+\frac{x+1}{(x-1)(x+1)}$
Combine the fractions:
$=\frac{x-1+x+1}{(x-1)(x+1)}$
Collect the like terms:
$=\frac{2x}{(x-1)(x+1)}$
