# How do you simplify (7x+14)/(7x^2-7x-42)?

Mar 27, 2018

$\textcolor{b l u e}{\frac{1}{x - 3}}$

#### Explanation:

$\frac{7 x + 14}{7 {x}^{2} - 7 x - 42}$

Factor out 7 from numerator and denominator:

$\frac{7 \left(x + 2\right)}{7 \left({x}^{2} - x - 6\right)}$

Cancel:

$\frac{\cancel{7} \left(x + 2\right)}{\cancel{7} \left({x}^{2} - x - 6\right)} = \frac{\left(x + 2\right)}{\left({x}^{2} - x - 6\right)}$

Factor denominator:

$\frac{\left(x + 2\right)}{\left(x + 2\right) \left(x - 3\right)}$

Cancel:

$\frac{\cancel{\left(x + 2\right)}}{\cancel{\left(x + 2\right)} \left(x - 3\right)} = \textcolor{b l u e}{\frac{1}{x - 3}}$

This result could also be achieved by factoring the denominator at the beginning, but this is a bit more difficult than factoring in stages: