# How do you simplify (sqrt5+2)/sqrt5-2)?

Dec 2, 2015

$\frac{2 \sqrt{5}}{5} - 1$

#### Explanation:

Simplify $\frac{\sqrt{5} + 2}{\sqrt{5}}$.

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

Therefore, when we add that to the original expression:

(1+(2sqrt5)/5)-2=color(blue)((2sqrt5)/5-1

This can also be written as:

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