# How do you simplify (9x^3)/(12x-24)div(x^2+4x)/(x-2)?

Nov 11, 2016

$\frac{3 {x}^{2}}{4 \left(x + 4\right)}$

#### Explanation:

The first step is to factor where possible and to change the division to a multiplication by the reciprocal

$\frac{9 {x}^{3}}{12 \left(x - 2\right)} \times \frac{x - 2}{x \left(x + 4\right)} \text{ } \leftarrow$ take out common factors

$\frac{9 {x}^{3}}{12 \left(\cancel{x - 2}\right)} \times \frac{\cancel{\left(x - 2\right)}}{x \left(x + 4\right)} \text{ } \leftarrow$ simplify

$\frac{3 {x}^{2}}{4 \left(x + 4\right)}$