# How do you simplify (4(x^2) - 36) / (x^2 + 10x + 21) and what are the restrictions?

Jul 13, 2015

First you factorise, then you may cancel.

#### Explanation:

$= \frac{4 \cdot \left({x}^{2} - 9\right)}{\left(x + 3\right) \left(x + 7\right)} = \frac{4 \cancel{\left(x + 3\right)} \left(x - 3\right)}{\cancel{\left(x + 3\right)} \left(x + 7\right)}$

$= \frac{4 \left(x - 3\right)}{x + 7}$

Restrictions : $x \ne - 3 \mathmr{and} x \ne - 7$
as these would make the denominator of the original $= 0$
$x = - 3$ is the worst, as this would create a $\frac{0}{0}$ situation, a capital sin in maths.