# How do you divide \frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }?

Apr 20, 2017

$\frac{5}{3 {n}^{3} + 3 {n}^{2}} \div \frac{1}{3 {n}^{2}} = \frac{5}{n + 1}$

#### Explanation:

$\frac{5}{3 {n}^{3} + 3 {n}^{2}} \div \frac{1}{3 {n}^{2}}$

Factor the denominator of the first fraction
$= \frac{5}{\left(3 {n}^{2}\right) \left(n + 1\right)} \div \frac{1}{3 {n}^{2}}$

Dividing is the same as multiplying by the reciprocal:
$= \frac{5}{\textcolor{red}{\left(3 {n}^{2}\right)} \left(n + 1\right)} \cdot \textcolor{red}{\left(3 {n}^{2}\right)}$

Cancel terms that are repeated on the numerator and denominator:
$= \frac{5}{n + 1}$