## Introductory Algebra for College Students (7th Edition)

$\displaystyle \frac{x^{2}-x-6}{x+2}$
In order to simplify, we have to 1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. Factoring $x^{2}-x-6$, we search for two factors of -6 whose sum is -1... ... these are $-3$ and $+2$ . $x^{2}-x-6=(x-3)(x+2)$ Placing $(x+2)$ in the denominator, we will be able to divide both the numerator and the denominator by $(x+2)$. What remains is $=(x-3)$ $\displaystyle \frac{x^{2}-x-6}{x+2}=\frac{(x-3)(x+2)}{(x+2)}=\frac{x-3}{1}=x-3$