# How do you rationalize the denominator and simplify 6/(sqrt4-sqrt14)?

Mar 27, 2018

$\frac{6}{\sqrt{4} - \sqrt{14}} = - \frac{3}{5} \left(\sqrt{4} + \sqrt{14}\right)$

#### Explanation:

To rationalise a surd, we multiply the denominator and numerator by its conjugate.

The conjugate of $\sqrt{a} + \sqrt{b}$ is $\sqrt{a} - \sqrt{b}$.

So,

$\frac{6}{\sqrt{4} - \sqrt{14}}$

$= \frac{6 \left(\sqrt{4} + \sqrt{14}\right)}{\left(\sqrt{4} - \sqrt{14}\right) \left(\sqrt{4} + \sqrt{14}\right)}$

$= \frac{6 \left(\sqrt{4} + \sqrt{14}\right)}{4 - 14}$

$= \frac{6}{-} 10 \left(\sqrt{4} + \sqrt{14}\right)$

$= - \frac{3}{5} \left(\sqrt{4} + \sqrt{14}\right)$