# How do you simplify (6a+18)/(9a+27)?

Feb 16, 2017

Se the entire simplification process below:

#### Explanation:

First, factor the numerator and denominator as:

$\frac{6 a + 18}{9 a + 27} = \frac{6 \left(a + 3\right)}{9 \left(a + 3\right)} = \frac{\left(3 \times 2\right) \left(a + 3\right)}{\left(3 \times 3\right) \left(a + 3\right)}$

We can now cancel common terms in the numerator and denominator:

$\frac{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 2\right) \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{\left(a + 3\right)}}}}{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 3\right) \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{\left(a + 3\right)}}}} = \frac{2}{3}$

However, because $9 a + 27$ cannot equal $0$ the complete answer is:

$\frac{2}{3}$ where $a \ne - 3$