Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 581: 44

$= \frac{2t}{(t+2)}$

$\frac{t^{2}+8t+15}{t^{2}-9} \times \frac{2t^{2}-6t}{t^{2}+7t+10}$ $= \frac{(t+3)(t+5)}{(t-3)(t+3)} \times \frac{2t(t-3)}{(t+5)(t+2)}$ $= \frac{(t+3)(t+5)}{(t+3)} \times \frac{2t}{(t+5)(t+2)}$ $= \frac{(t+5)}{1} \times \frac{2t}{(t+5)(t+2)}$ $= \frac{2t(t+5)}{(t+5)(t+2)}$ $= \frac{2t}{(t+2)}$