# How do you rationalize the denominator and simplify 3/(2-sqrt5)?

Jun 19, 2017

When given a fraction of the form:

c/(a-sqrt(b)

You rationalize the denominator by multiplying by 1 in the form $\frac{a + \sqrt{b}}{a + \sqrt{b}}$

#### Explanation:

Multiply the fraction by 1 in the form $\frac{2 + \sqrt{5}}{2 + \sqrt{5}}$:

$\frac{3}{2 - \sqrt{5}} \frac{2 + \sqrt{5}}{2 + \sqrt{5}}$

$\frac{3 \left(2 + \sqrt{5}\right)}{{2}^{2} - {\left(\sqrt{5}\right)}^{2}}$

$\frac{3 \left(2 + \sqrt{5}\right)}{4 - 5}$

$- 3 \left(2 + \sqrt{5}\right)$

$- 6 - 3 \sqrt{5}$