# How do you divide \frac { \frac { 6u } { u ^ { 2} + 2u - 35} } { \frac { 2} { u - 5} }?

Mar 29, 2017

$\frac{3 u}{u + 7}$

#### Explanation:

Rewrite it as a division question:

$\frac{6 u}{{u}^{2} + 2 u - 35} \div \frac{2}{u - 5}$

Flip the fraction on the right side and rewrite it as a multiplication question:

$\frac{6 u}{{u}^{2} + 2 u - 35} \times \frac{u - 5}{2}$

Factor out a $u - 5$ from the bottom of the left fraction and cancel it with the other other $u - 5$:

$\frac{6 u}{u + 7} \times \frac{1}{2}$

Now take $2$ out of $6$. You're left with $\frac{1}{1}$ on the right side so that doesn't matter. So you have:

$\frac{3 u}{u + 7}$