Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 580: 32

$= -\frac{4(n+6)}{(2n-3)}$

$\frac{2n+12}{4-3n} \div \frac{4n-6}{12n-16}$ $= \frac{2n+12}{4-3n} \times \frac{12n-16}{4n-6}$ $= \frac{2(n+6)}{4-3n} \times \frac{4(3n-4)}{2(2n-3)}$ $= \frac{2(n+6)}{4-3n} \times \frac{4(-(4-3n))}{2(2n-3)}$ $= \frac{2(n+6)}{1} \times \frac{-4}{2(2n-3)}$ $= -\frac{4(n+6)}{(2n-3)}$