# How do you simplify (k^2-4)/(3k^2) ÷ (2-k)/(11k)?

Jul 22, 2015

$- \frac{11}{3} \left(\frac{k + 2}{k}\right)$

#### Explanation:

First convert the division to a multiplication by inverting the second fraction:
(k^2-4)/(3k^2)÷(2-k)/(11k)=(k^2-4)/(3k^2)(11k)/(2-k)

Factor all the terms:
$\frac{{k}^{2} - 4}{3 {k}^{2}} \cdot \frac{11 k}{2 - k} = - \frac{\left(k - 2\right) \left(k + 2\right)}{3 {k}^{2}} \frac{11 k}{k - 2}$

Cancel similar terms:
$- \frac{\left(k - 2\right) \left(k + 2\right)}{3 {k}^{2}} \frac{11 k}{k - 2} = - \frac{11}{3} \left(\frac{k + 2}{k}\right)$