Question

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

Answer 1

I got as far as: `-5/2*(sqrt(3)-sqrt(5))`

Explanation:

You can multiply and divide by `sqrt(3)-sqrt(5)` and take advantage of the fact that: `(a+b)(a-b)=a^2-b^2` and write:

`5/(sqrt(3)+sqrt(5))*color(red)((sqrt(3)-sqrt(5))/(sqrt(3)-sqrt(5))=`

`=(5*(sqrt(3)-sqrt(5)))/(3-5)=-5/2*(sqrt(3)-sqrt(5))`