# How do you simplify (q^2+14q+48)/(q^2+q-30)?

Oct 14, 2015

$\frac{q + 8}{q - 5}$ for $q \ne - 6$ and $q \ne 5$

#### Explanation:

Notice that
${q}^{2} + 14 q + 48 = \left(q + 6\right) \left(q + 8\right)$
and
${q}^{2} + q - 30 = \left(q + 6\right) \left(q - 5\right)$

Therefore,
$\frac{{q}^{2} + 14 q + 48}{{q}^{2} + q - 30} = \frac{\left(q + 6\right) \left(q + 8\right)}{\left(q + 6\right) \left(q - 5\right)}$

This expression is not defined for
$q = - 6$ and $q = 5$

For all other values of $q$ we can reduce it by $q + 6$ to
$\frac{q + 8}{q - 5}$