# How do you simplify (15a+5b)/(5ab) div 3a+b?

Jul 14, 2015

$\frac{15 a + 5 b}{5 a b} \div \left(3 a + b\right) = \frac{1}{a b}$
$\textcolor{w h i t e}{\text{XXXX}}$Warning: this is not exactly what was asked, but I think it was what was intended.

#### Explanation:

$\frac{15 a + 5 b}{5 a b} \div \left(3 a + b\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{15 a + 5 b}{5 a b} \times \frac{1}{3 a + b}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{5 \left(3 a + b\right)}{5 \left(a b\right)} \times \frac{1}{3 a + b}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{\cancel{5} \left(\cancel{3 a + b}\right)}{\cancel{5} \left(a b\right)} \times \frac{1}{\cancel{3 a + b}}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{1}{a b}$

Technically what was asked should have been evaluated as
$\textcolor{w h i t e}{\text{XXXX}}$$\left(\frac{15 a + 5 b}{5 a b} \times \frac{1}{3 a}\right) + 2$
Please repost, if that is what you intended.