# How do you divide \frac { x ^ { 2} - 4} { x ^ { 2} + 7x + 10} \div \frac { x } { x + 5}?

Jun 18, 2018

$\frac{x - 2}{x}$

#### Explanation:

$\setminus \frac{{x}^{2} - 4}{{x}^{2} + 7 x + 10} \setminus \div \setminus \frac{x}{x + 5}$

is the same thing as inverting and multiplying:

$\frac{{x}^{2} - 4}{{x}^{2} + 7 x + 10} \cdot \frac{x + 5}{x}$

Now let's factor and see if we can remove some terms:

$\frac{\left(x - 2\right) \left(x + 2\right)}{\left(x + 5\right) \left(x + 2\right)} \cdot \frac{x + 5}{x}$

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

$\frac{x - 2}{x}$