# How do you divide (5x+15)/(12x-6) div(10x^2)/(18)?

Aug 30, 2015

$\frac{3}{2} \cdot \frac{x + 3}{x - 2} \cdot \frac{1}{x} ^ 2$

#### Explanation:

Your starting expression looks like this

$\frac{5 x + 15}{12 x - 6} \cdot \frac{18}{10 {x}^{2}}$

Factor the numerator and the denominator of the first fraction to get

$\frac{5 \left(x + 3\right)}{6 \left(x - 2\right)}$

The expression will now become

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \left(x + 3\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} \left(x - 2\right)} \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{18}}} 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} 2 {x}^{2}}$

$\frac{x + 3}{x - 2} \cdot \frac{3}{2 {x}^{2}} = \textcolor{g r e e n}{\frac{3}{2} \cdot \frac{x + 3}{x - 2} \cdot \frac{1}{x} ^ 2}$