Question

How do you simplify `(sqrt5+3)/(4-sqrt5)`?

Answer 1

`17/11 + [7sqrt5]/11`

Explanation:

`[sqrt5 + 3]/[4 - sqrt5] = [sqrt5 + 3]/[4 - sqrt5] * [4 + sqrt5]/[4 + sqrt5] = [4sqrt5 + 12 + 5 + 3sqrt5]/[16 - 5]=[17 + 7sqrt5]/11 = 17/11 +[ 7sqrt5]/11`