Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 581: 46

$= \frac{(r-3)}{(r+5)}$

$\frac{r^{2}-36}{r^{2}-11r+30} \div \frac{r^{2}+11r+30}{r^{2}-8r+15}$ $= \frac{r^{2}-36}{r^{2}-11r+30} \times \frac{r^{2}-8r+15}{r^{2}+11r+30}$ $= \frac{(r-6)(r+6)}{(r-6)(r-5)} \times \frac{(r-3)(r-5)}{(r+6)(r+5)}$ $= \frac{(r+6)}{(r-5)} \times \frac{(r-3)(r-5)}{(r+6)(r+5)}$ $= \frac{(r+6)}{1} \times \frac{(r-3)}{(r+6)(r+5)}$ $= \frac{1}{1} \times \frac{(r-3)}{(r+5)}$ $= 1\times \frac{(r-3)}{(r+5)}$ $= \frac{(r-3)}{(r+5)}$