Question

How do you simplify `(sqrt7+sqrt3)/(sqrt7-sqrt3)`?

Answer 1

`(sqrt7+sqrt3)^2/4`

Explanation:

Multiply both sides by `(sqrt7+sqrt3)/(sqrt7+sqrt3)`

`(sqrt7+sqrt3)/(sqrt7-sqrt3) xx (sqrt7+sqrt3)/(sqrt7+sqrt3)`

The bottom shows the factors of the difference of squares.

`(sqrt7+sqrt3)^2/(sqrt7^2 - sqrt3^2) = (sqrt7+sqrt3)^2/(7-3)`

`(sqrt7+sqrt3)^2/4`