Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 581: 42

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

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