# How do you simplify \frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}?

Aug 9, 2017

8/(x+5

#### Explanation:

First, we get rid of the division symbols by turning them into multiplication by getting the reciprocal of the fraction, giving us a new equation of

$\frac{8 x}{{x}^{2} - 9 x + 14} \times \frac{{x}^{2} - 4}{{x}^{2} + 5 x} \times \frac{x - 7}{x + 2}$

We then factorise all the values we can to their simplest form, giving us

$\frac{8 x}{\left(x - 7\right) \left(x - 2\right)} \times \frac{\left(x - 2\right) \left(x + 2\right)}{x \left(x + 5\right)} \times \frac{x - 7}{x + 2}$

We then get rid of common factors, simplifying the equation down to

$\frac{8}{1} \times \frac{1}{\left(x + 5\right)} \times \frac{1}{1}$

8/(x+5