# How do you rationalize the denominator and simplify 5/(sqrt3+sqrt5)?

I got as far as: $- \frac{5}{2} \cdot \left(\sqrt{3} - \sqrt{5}\right)$
You can multiply and divide by $\sqrt{3} - \sqrt{5}$ and take advantage of the fact that: $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$ and write:
5/(sqrt(3)+sqrt(5))*color(red)((sqrt(3)-sqrt(5))/(sqrt(3)-sqrt(5))=
$= \frac{5 \cdot \left(\sqrt{3} - \sqrt{5}\right)}{3 - 5} = - \frac{5}{2} \cdot \left(\sqrt{3} - \sqrt{5}\right)$