# How do you rationalize the denominator and simplify (sqrt5+2)/(3sqrt5-1)?

Apr 18, 2016

$\frac{13 + 5 \sqrt{5}}{44}$

#### Explanation:

To rationalize, multiply with the conjugate of denominator, $3 \sqrt{5} + 1$ both in denominator and numerator. The result would be

$\frac{\left(\sqrt{5} + 2\right) \left(3 \sqrt{5} - 1\right)}{45 - 1}$

=$\frac{15 + 5 \sqrt{5} - 2}{44}$

=$\frac{13 + 5 \sqrt{5}}{44}$

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