# How do you simplify (8-x)/(x^2-7x-8)?

Mar 22, 2018

$- \frac{1}{x + 1}$

#### Explanation:

Lets begin by factoring the quadratic in the denominator:

${x}^{2} - 7 x - 8 = \left(x - 8\right) \left(x + 1\right)$

The first factor is, in fact, the negative of the numerator:

$8 - x = - \left(x - 8\right)$

So we can rewrite our fraction as:

$\frac{- \left(x - 8\right)}{\left(x - 8\right) \left(x + 1\right)}$

Finally

$- \frac{1}{x + 1}$