Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set - Page 517: 66

$\frac{9}{4(x-1)}$

$\frac{9}{x^{2}-1}$ $\div$ $\frac{12}{3x+3}$= $\frac{9}{(x+1)(x-1)}$ $\times$ $\frac{3x+3}{12}$= $\frac{9}{(x+1)(x-1)}$ $\times$ $\frac{3(x+1)}{12}$= $\frac{9*3(x+1)}{(x+1)(x-1)12}$ =$\frac{27}{12(x-1)}$= $\frac{9}{4(x-1)}$