Rationalize the denominator & simplify

Question

The answer I got was: 2.

Is this correct?

Answer 1

Yes, the denominator simplifies to 2 when rationalized, but I think the problem wants you to rationalize the denominator then simplify the whole expression. To simplify the whole expression, multiply top and bottom by the conjugate of the denominator, √3 - 1.

4(√3 - 1) / (√3 + 1)(√3 - 1)

= 4(√3 - 1) / 2

= 2(√3 - 1)

= 2√3 - 2