Answer
$\frac{3h^2+2h(t+2)}{2((t-2)(t+2))}$
Work Step by Step
$\frac{3h^2}{2t^2-8}+ \frac{h}{t-2}$
$\frac{3h^2}{2(t^2-4)}+ \frac{h}{t-2}$
$\frac{3h^2}{2((t-2)(t+2))}+ \frac{h}{t-2}$
$\frac{3h^2}{2((t-2)(t+2))}+ (\frac{h}{t-2}*\frac{2(t+2)}{2(t+2)})$
$\frac{3h^2}{2((t-2)(t+2))}+ (\frac{2h(t+2)}{2(t+2)(t-2)})$
$\frac{3h^2+2h(t+2)}{2((t-2)(t+2))}$