Question

How do you rationalize the denominator and simplify `(6sqrt3 - sqrt7) /( 4 - sqrt3)`?

Answer 1

`((4+sqrt3)(6sqrt3-sqrt7))/13`

Explanation:

`(6sqrt(3)-sqrt(7))/(4-sqrt(3))=(6sqrt(3)-sqrt(7))/(4-sqrt(3))((4+sqrt3)/(4+sqrt3))`

`=((4+sqrt3)(6sqrt3-sqrt7))/(16-3)`

`=((4+sqrt3)(6sqrt3-sqrt7))/13`