# How do you simplify (x^2-25) / (2x) div (x^2 + 6x+5) / (4x^2)?

May 22, 2017

First we change this into a multiplication, by inverting the second term.

#### Explanation:

Inverting means swapping the stuff below and above the division bar:

$= \frac{{x}^{2} - 25}{2 x} \times \frac{4 {x}^{2}}{{x}^{2} + 6 x + 5}$

Now, if we factorize, we may cancel some parts:

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

$= \frac{2 x \left(x - 5\right)}{x + 1} = \frac{4 {x}^{2} - 10 x}{x + 1}$