# How do you divide and simplify \frac { m ^ { 2} } { m - 2} \div \frac { m ^ { 2} - 3m } { m ^ { 2} - 5m + 6}?

Mar 10, 2018

$m$

#### Explanation:

We have the problem:

${m}^{2} / \left(m - 2\right) \div \frac{{m}^{2} - 3 m}{{m}^{2} - 5 m + 6}$

1) Reciprocate the second term, and change the sign:

$\implies {m}^{2} / \left(m - 2\right) \cdot \frac{{m}^{2} - 5 m + 6}{{m}^{2} - 3 m}$

2) Factorize the terms:

$\frac{\left(m\right) \left(m\right)}{\left(m - 2\right)} \cdot \frac{\left(m - 3\right) \left(m - 2\right)}{\left(m\right) \left(m - 3\right)}$

Cancelling out:

$\frac{\cancel{\left(m\right)} \left(m\right)}{\cancel{\left(m - 2\right)}} \cdot \frac{\cancel{\left(m - 3\right)} \cancel{\left(m - 2\right)}}{\cancel{\left(m\right)} \cancel{\left(m - 3\right)}}$

$= \frac{m}{1} \cdot \frac{1}{1}$

$= 1 m$

$= m$

Thus, solved.