Question

How do you simplify `(2 - sqrt5) / (3 +sqrt5)`?

Answer 1

`(2-sqrt5)/(3+sqrt5)=(11-5sqrt5)/4`

Explanation:

`(2-sqrt5)/(3+sqrt5)`

`((2-sqrt5)(3-sqrt5))/((3+sqrt5)(3-sqrt5))=(6-2sqrt5-3sqrt5+(sqrt5)^2)/(3^2-(sqrt5)^2)`

`(6-5sqrt5+5)/(9-5)=(11-5sqrt5)/4`

`(2-sqrt5)/(3+sqrt5)=(11-5sqrt5)/4`