Answer
$\frac{2x+2}{(x+2)(x-2)}$
Work Step by Step
$\frac{x}{x^{2}-4}+\frac{1}{x-2}$
Factorise $x^{2}-4$ and replace in fraction:
$=\frac{x}{(x+2)(x-2)}+\frac{1}{x-2}$
Find the lowest common denominator (i.e. $(x+2)(x-2)$) and adjust accordingly:
$=\frac{x}{(x+2)(x-2)}+\frac{1\times (x+2)}{(x-2)\times (x+2)}$
$=\frac{x}{(x+2)(x-2)}+\frac{x+2}{(x-2)(x+2)}$
Combine the fractions:
$=\frac{x+x+2}{(x+2)(x-2)}$
Simplify:
$=\frac{2x+2}{(x+2)(x-2)}$
