# How do you find the quotient of (b^2+6b+5)/(6b+6)div(b+5)?

Sep 20, 2017

$\frac{1}{6}$

#### Explanation:

The first step with algebraic fractions is to factorise wherever possible:

$\frac{{b}^{2} + 6 b + 5}{6 b + 6} \textcolor{b l u e}{\div \frac{\left(b + 5\right)}{1}}$

$= \frac{\left(b + 5\right) \left(b + 1\right)}{6 \left(b + 1\right)} \textcolor{b l u e}{\times \frac{1}{\left(b + 5\right)}} \text{ } \leftarrow$ multiply by the reciprocal

$= \frac{\cancel{\left(b + 5\right)} \cancel{\left(b + 1\right)}}{6 \cancel{\left(b + 1\right)}} \times \frac{1}{\cancel{\left(b + 5\right)}} \text{ } \leftarrow$ cancel like factors

$= \frac{1}{6}$