# How do you divide \frac { ( m - 2) ^ { 2} } { n ^ { 2} } \div \frac { 8m - 16} { 4n }?

Feb 18, 2017

$\frac{m - 2}{2 n}$

#### Explanation:

Remember, you can change a division problem to a multiplication problem when you reciprocate the second term:

$\frac{{\left(m - 2\right)}^{2}}{n} ^ 2 \div \frac{8 m - 16}{4 n} = \frac{{\left(m - 2\right)}^{2}}{n} ^ 2 \cdot \frac{4 n}{8 m - 16}$

Factor the second terms denominator: $\frac{{\left(m - 2\right)}^{2}}{n} ^ 2 \cdot \frac{4 n}{8 \left(m - 2\right)}$

Rearrange & Simplify: $\frac{4 n}{8 {n}^{2}} \cdot {\left(m - 2\right)}^{2} / \left(m - 2\right) = \frac{m - 2}{2 n}$