# How do you rationalize the denominator and simplify 5/(sqrt6-2)?

Aug 5, 2018

I tried this:

#### Explanation:

Let us multiply and divide by $\sqrt{6} + 2$:

$\frac{5}{\sqrt{6} - 2} \cdot \textcolor{red}{\frac{\sqrt{6} + 2}{\sqrt{6} + 2}}$

$= \frac{5 \sqrt{6} + 10}{6 - 4}$

$= \frac{5 \sqrt{6} + 10}{2}$

$= \frac{5}{2} \sqrt{6} + 5$

$= 5 \left(\frac{\sqrt{6}}{2} + 1\right)$