Answer
$\displaystyle \frac{13}{6(x+2)},\quad x\neq-2$
Work Step by Step
Factor each denominator.
$\displaystyle \frac{3}{2x+4}+\frac{2}{3x+6}=\frac{3}{2(x+2)}+\frac{2}{3(x+2)}$
The denominators are different. Find a common denominator.
LCD=$2(x+2)\cdot 3=6(x+2)$
$=\displaystyle \frac{3}{2(x+2)}\times\frac{3}{3}+\frac{2}{3(x+2)}\times\frac{2}{2}$
$=\displaystyle \frac{9}{6(x+2)}+\frac{4}{6(x+2)}$
$=\displaystyle \frac{9+4}{6(x+2)}$
=$\displaystyle \frac{13}{6(x+2)},\quad x\neq-2$
