# How do you rationalize the denominator and simplify 4/(sqrt7-sqrt5)?

Nov 12, 2017

$= 2 \left(\sqrt{7} + \sqrt{5}\right)$

#### Explanation:

$\frac{4}{\sqrt{7} - \sqrt{5}}$

to rationalise the denominator we make use of

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

so

$\frac{4}{\sqrt{7} - \sqrt{5}} = \frac{4}{\sqrt{7} - \sqrt{5}} \times \frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}$

$= \frac{4 \left(\sqrt{7} + \sqrt{5}\right)}{{\left(\sqrt{7}\right)}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$= \frac{4 \left(\sqrt{7} + \sqrt{5}\right)}{7 - 5}$

$= \frac{{\cancel{4}}^{2} \left(\sqrt{7} + \sqrt{5}\right)}{\cancel{2}}$

$= 2 \left(\sqrt{7} + \sqrt{5}\right)$