Question

How do you rationalize the denominator and simplify `1/(sqrt3-sqrt5)`?

Answer 1

The expression can be simplified to `-(sqrt(3) + sqrt(5))/2`.

Explanation:

Multiply the entire expression by the conjugate of the denominator. The conjugate can be found by switching the middle sign in the denominator (when the denominator is a binomial , of course).

`=>1/(sqrt(3) - sqrt(5)) xx (sqrt(3) + sqrt(5))/(sqrt(3) + sqrt(5))`

`=>(sqrt(3) + sqrt(5))/(sqrt(9) - sqrt(25))`

`=>(sqrt(3) + sqrt(5))/(3 - 5)`

`=>(sqrt(3) + sqrt(5))/(-2)`

`=> -(sqrt(3) + sqrt(5))/2`

Hopefully this helps!