Question

How do you simplify `5/(sqrt[3] + sqrt[5])`?

Answer 1

`\frac{5}{2}(\sqrt5-\sqrt3)`

Explanation:

`\frac{5}{\sqrt3+\sqrt5}`

`=\frac{5}{\sqrt5+\sqrt3}`

`=\frac{5(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}`

`=\frac{5(\sqrt5-\sqrt3)}{(\sqrt5)^2-(\sqrt3)^2}`

`=\frac{5(\sqrt5-\sqrt3)}{5-3}`

`=\frac{5}{2}(\sqrt5-\sqrt3)`