# How do you simplify (5x^2+10x)/(x^2-x-6)div(15x^3+45x^2)/(x^2-9)?

Feb 19, 2017

$\frac{1}{3 x}$

#### Explanation:

To simplify, it is advisable to factorise the expressions first and then see if some get cancelled out.

=$\frac{5 x \left(x + 2\right)}{\left(x - 3\right) \left(x + 2\right)} \div \frac{15 {x}^{2} \left(x + 3\right)}{\left(x - 3\right) \left(x + 3\right)}$

=$\frac{5 x}{x - 3} \div \frac{15 {x}^{2}}{x - 3}$

=$\frac{5 x}{x - 3} \cdot \frac{x - 3}{15 {x}^{2}}$

= $\frac{1}{3 x}$