# How do you rationalize the denominator and simplify (3 sqrt 5 + 2) / (3 sqrt 5 + 5)?

Mar 13, 2016

$\frac{1}{20} \left(35 - 9 \sqrt{5}\right)$

#### Explanation:

multiplying by $3 \sqrt{5} - 5$ on both numerator and denominator we get $\frac{\left(3 \sqrt{5} + 2\right) \cdot \left(3 \sqrt{5} - 5\right)}{45 - 25}$=$\left(\frac{45 - 10 - \sqrt{5} \left(15 - 6\right)}{20}\right)$ = $\frac{1}{20} \left(35 - 9 \sqrt{5}\right)$[answer]