Question

Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`

Answer 1

 We know that rationalization factor for `3 + sqrt5` and `3 - sqrt5` are `3 - sqrt5` and `3 + sqrt5`respectively.

We will multiply numerator and denominator of the given expression  `(7 + 3sqrt5)/(3 + sqrt5)` and `(7 - 3sqrt5)/(3 - sqrt5)` by `3 - sqrt5` ans `3 + sqrt5` respectively, to get

`(7 + 3sqrt5)/(3 + sqrt5) xx (3 - sqrt5)/(3 - sqrt5) - (7 - 3sqrt5)/(3 - sqrt5) xx (3 + sqrt5)/(3 + sqrt5)`