Simplify Please?

Question

Hello,

There is a question that I am not sure how to do:

Simplify: 1 / (√3 + 1) + 1 / (√3 - 1)

The answer is apparently √3

Thank you in advance.

Answer 1

1 / (√3 + 1) + 1 / (√3 - 1)

LCM of (√3 + 1) and (√3 - 1) is (√3 + 1)(√3 - 1).

=(√3 - 1+√3 + 1) / (√3 + 1) (√3 - 1)

=2√3/((√3)²-(1)²)                                                (Since ( a+b)(a-b)  =a²-b²)

=2√3/(3-1)    

  =2√3/2  

  =√3