# How do you divide  (x^2-5x-14)/(x-7)div(x+2)/(x^2-9)?

##### 1 Answer
May 22, 2015

Dividing is the same as multiplying by the reciprocal.

So
$\frac{{x}^{2} - 5 x - 14}{x - 7} \div \frac{x + 2}{{x}^{2} - 9}$
is the same as
$\frac{{x}^{2} - 5 x - 14}{x - 7} \times \frac{{x}^{2} - 9}{x + 2}$

We can simplify this by factoring

$\frac{\left(x - 7\right) \left(x + 2\right)}{x - 7} \times \frac{{x}^{2} - 9}{x + 2}$

(cancel(color(red)((x-7)))cancel(color(blue)((x+2))))/cancel(color(red)((x-7)))xx(x^2-9)/cancel(color(blue)((x+2))

$= {x}^{2} - 9$