# How do you simplify the expression (4a^2b+8ab)/(6a^2-6a)?

May 20, 2017

See a solution process below:

#### Explanation:

First, rewrite the numerator and denominator by factoring out common terms:

$\frac{\left(4 a b \cdot a\right) + \left(4 a b \cdot 2\right)}{\left(6 a \cdot a\right) - \left(6 a \cdot 1\right)} \implies \frac{4 a b \left(a + 2\right)}{6 a \left(a - 1\right)}$

Now, cancel common terms in the numerator and denominator:

$\frac{4 a b \left(a + 2\right)}{6 a \left(a - 1\right)} \implies \frac{\left(2 \times 2\right) a b \left(a + 2\right)}{\left(2 \times 3\right) a \left(a - 1\right)} \implies$

$\frac{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 2\right) \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{a}}} b \left(a + 2\right)}{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 3\right) \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{a}}} \left(a - 1\right)} \implies \frac{2 b \left(a + 2\right)}{3 \left(a - 1\right)}$