# How do you multiply 1/(x^2-25) - (x+5)/(x^2-4x-5)?

Apr 19, 2018

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

#### Explanation:

I'm guessing that means you aren't subtracting, you meant to put a multiplication sign as follows:

$\frac{1}{{x}^{2} - 25} \cdot \frac{x + 5}{{x}^{2} - 4 x - 5}$

First, you would factor:

$\frac{1}{\left(x + 5\right) \left(x - 5\right)} \cdot \frac{x + 5}{\left(x - 5\right) \left(x + 1\right)}$

We see some terms cancel if they are both in the numerator and denominator:

$\frac{1}{\cancel{\left(x + 5\right)} \left(x - 5\right)} \cdot \frac{\cancel{x + 5}}{\left(x - 5\right) \left(x + 1\right)}$

This gives us:

$\frac{1}{x - 5} \cdot \frac{1}{\left(x - 5\right) \left(x + 1\right)}$

Which simplifies to:

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