Question

How do you simplify `(2+sqrt3)/(2-sqrt3)`?

Answer 1

Multiply both numerator and denominator of the fraction by the conjugate of the denominator to clear the square root from the denominator.

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

`=(2+sqrt(3))/(2-sqrt(3)) *(2+sqrt(3))/(2+sqrt(3))`

`=(4+4sqrt(3)+3)/(4-3)`

`= 7+4sqrt(3)`