Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 581: 34

$= \frac{(m+6)}{(m-12)}$

$\frac{(m+7)(m-5)}{(m+2)(m+7)} \div \frac{(m-5)(m-12)}{(m+2)(m+6)}$ $= \frac{(m+7)(m-5)}{(m+2)(m+7)} \times \frac{(m+2)(m+6)}{(m-5)(m-12)}$ $= \frac{(m+7)(m-5)}{(m+7)} \times \frac{(m+6)}{(m-5)(m-12)}$ $= 1\times \frac{(m+6)}{(m-12)}$ $= \frac{(m+6)}{(m-12)}$