# How do you simplify (x^2+4x-5)/(x^2-1)?

Jan 24, 2017

Factor the numerator and the denominator, and see if you can cancel any of the factors!

#### Explanation:

$\frac{\left(x + 5\right) \left(x - 1\right)}{\left(x + 1\right) \left(x - 1\right)}$ reduces by canceling out the repeated (x-1) that appears in both top and bottom of the expression.

Your final answer is: $\frac{x + 5}{x + 1}$.

Jan 24, 2017

The answer is $= \frac{x + 5}{x + 1}$

#### Explanation:

We need

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

Let's factorise the numerator and denominator

${x}^{2} + 4 x - 5 = \left(x - 1\right) \left(x + 5\right)$

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

Therefore,

$\frac{{x}^{2} + 4 x - 5}{{x}^{2} - 1} = \frac{\cancel{x - 1} \left(x + 5\right)}{\left(x + 1\right) \cancel{x - 1}}$

$= \frac{x + 5}{x + 1}$