Chapter 11 - Rational Expressions and Functions - 11-2 Multiplying and Dividing Rational Expressions - Practice and Problem-Solving Exercises - Page 675: 55

$\frac{x-2}{x-3}, with$ $x\ne3$

Given : $\frac{x^{2}+x-6}{x^{2}-x-6} \div \frac{x^{2}+5x+6}{x^{2}+4x+4}=\frac{(x+3)(x-2)}{(x-3)(x+2)} \times \frac{(x+2)(x+2)}{(x+2)(x+3)}$ This becomes : $\frac{x-2}{x-3}$ (After dividing out the common factors (x+2) and (x+3))