Answer
$\frac{2(x+1)}{(x-2)(x+2)}$
Work Step by Step
We form a common denominator, then add, factor, and simplify:
$\displaystyle \frac{x}{x^{2}-4}+\frac{1}{x-2}=\frac{x}{(x-2)(x+2)}+\frac{1}{x-2}=\frac{x}{(x-2)(x+2)}+\frac{x+2}{(x-2)(x+2)}
=\frac{2x+2}{(x-2)(x+2)}=\frac{2(x+1)}{(x-2)(x+2)}$
