#### Answer

$\frac{4x}{9}$

#### Work Step by Step

By inspection, we see that the LCM of the denominators is $9$. Therefore, we create a common denominator using this LCM and obtain:
$\frac{x-6}{9}+\frac{x+2}{3}$
=$\frac{1(x-6)+3(x+2)}{9}$
=$\frac{x-6+3x+6}{9}$
=$\frac{4x+0}{9}$
=$\frac{4x}{9}$