# How do you simplify (x^2+3x-18)/(x^2-36)?

Oct 18, 2015

(x^2 + 3x − 18) / (x^2 − 36) = (x - 3) / (x - 6) only if x $\ne - 6$

#### Explanation:

x^2 + 3x − 18  can be written as
$\left(x + 6\right) \cdot \left(x - 3\right)$ and
x^2 − 36 can be written as $\left(x + 6\right) \cdot \left(x - 6\right)$
So,
(x^2 + 3x − 18) / (x^2 − 36) = ((x + 6) * (x - 3)) / ((x + 6) * (x - 6))
We can cancel $x + 6$ only if $x + 6 \ne 0 \mathmr{and} \mathmr{if} x \ne - 6$
If $x \ne - 6$, the expression becomes
$\frac{x - 3}{x - 6}$
If x = -6, it is indeterminate ( 0 / 0 form)