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

Usually, when you want to rationalize a binomial denominator you will multiply it by its conjugate, in this case $\left(3 \sqrt{5} - 5\right)$.
As you know, in order to preserve the fraction, you will multiply it by 1, which is the same as $\frac{3 \sqrt{5} - 5}{3 \sqrt{5} - 5}$.
$\frac{\left(3 \sqrt{5} + 2\right)}{\left(3 \sqrt{5} + 5\right)} \frac{\left(3 \sqrt{5} - 5\right)}{\left(3 \sqrt{5} - 5\right)} = \frac{45 - 15 \sqrt{5} + 6 \sqrt{5} - 10}{45 - 25} = \frac{35 - 11 \sqrt{5}}{20}$