# How do you simplify (x^2 – 6x – 7 )/( x^2 – 1)?

Oct 7, 2015

$\frac{x - 7}{x - 1}$

#### Explanation:

Notice that you can rewrite the numerator of the fraction as

${x}^{2} - 6 x - 7 = {x}^{2} - 7 x + x - 7$

$= x \left(x - 7\right) + \left(x - 7\right) = \left(x - 7\right) \left(x + 1\right)$

The denominator of the fraction can be rewritten as

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

This means that the expression becomes

$\frac{\cancel{\left(x + 1\right)} \cdot \left(x - 7\right)}{\cancel{\left(x + 1\right)} \cdot \left(x - 1\right)} = \textcolor{g r e e n}{\frac{x - 7}{x - 1}}$