#### Answer

$= \frac{(t+10)(t+2)(t-2)}{(t+7)(t-10)(t+1)}$

#### Work Step by Step

$\frac{t^{2}+12t+20}{t^{2}-49} \div \frac{t^{2}-100}{t^{2}-9t+14}$
$= \frac{t^{2}+12t+20}{t^{2}-49} \times \frac{t^{2}-9t+14}{t^{2}-100}$
$= \frac{(t+10)(t+2)}{(t-7)(t+7)} \times \frac{(t-7)(t-2)}{(t-10)(t+1)}$
$= \frac{(t+10)(t+2)}{(t+7)} \times \frac{(t-2)}{(t-10)(t+1)}$
$= \frac{(t+10)(t+2)(t-2)}{(t+7)(t-10)(t+1)}$