Question

simplify.
$\frac{x - 2}{x^{2} + 4x - 12}$

Explanation:

Step1: Factor the denominator

Factor quadratic $x^2+4x-12$ into binomials:
$x^2+4x-12=(x+6)(x-2)$

Step2: Cancel common factors

Cancel $(x-2)$ from numerator and denominator (where $x
eq2$):
$\frac{x-2}{(x+6)(x-2)}=\frac{1}{x+6}$

Answer:

$\frac{1}{x+6}$ (where $x
eq2, x
eq-6$)