# How do you simplify the expression 4 over square root of 7 + the square root of 3?

Sep 15, 2015

$\left(\sqrt{7} - \sqrt{3}\right)$

#### Explanation:

$\frac{4}{\sqrt{7} + \sqrt{3}}$
$\textcolor{w h i t e}{\text{XXXXX}}$rationalizing the denominator:
$= \frac{4}{\sqrt{7} - \sqrt{3}} \times \frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} + \sqrt{3}}$

$= \frac{4 \left(\sqrt{7} + \sqrt{3}\right)}{{\left(\sqrt{7}\right)}^{2} - {\left(\sqrt{3}\right)}^{2}}$

$= \frac{4 \left(\sqrt{7} + \sqrt{3}\right)}{7 - 3}$

$= \frac{\cancel{4} \left(\sqrt{7} + \sqrt{3}\right)}{\cancel{4}}$