Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 580: 16

$= -\frac{(t+13)}{(t-13)} $

$\frac{(t+7)(t-9)}{(t+3)(t+7)} \times \frac{(t+3)(t+13)}{(9-t)(t-13)}$ $= \frac{(t+7)(t-9)(t+3)(t+13)}{(t+3)(t+7)(9-t)(t-13)} $ $= \frac{(t-9)(t+3)(t+13)}{(t+3)(9-t)(t-13)} $ $= \frac{(-(9-t))(t+13)}{(9-t)(t-13)} $ $= \frac{-(t+13)}{(t-13)} $ $= -\frac{(t+13)}{(t-13)} $