Answer
$\displaystyle \frac{x^{2}-x-6}{x+2}$
Work Step by Step
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 $=(x-3)$
$\displaystyle \frac{x^{2}-x-6}{x+2}=\frac{(x-3)(x+2)}{(x+2)}=\frac{x-3}{1}=x-3$
