if [sqrt(a) + sqrt(b)]/ [sqrt(a) – sqrt(b)] + [sqrt(a) – sqrt(b)]/ [sqrt(a) + sqrt(b)] = a – b, then prove that a – b = sqrt (2)

Hello student,
Please find the answer to your question below
Given
Taking lcm we get

On expanding we get
(a-b)²=2(a+b)
so you get (a-b)=
I think there is some error in the question