Answer
$\frac{x-2}{(x-3)(x+3)}$
Work Step by Step
We form a common denominator, then add, factor, and simplify:
$\displaystyle \frac{1}{x+3}+\frac{1}{x^{2}-9}=\frac{1}{x+3}+\frac{1}{(x-3)(x+3)}=\frac{x-3}{(x-3)(x+3)}+\frac{1}{(x-3)(x+3)}=\frac{x-2}{(x-3)(x+3)}$
