Simplify

1.
√y /(√x - √y) + √x /(√x + √y)
= √y(√x + √y)/(√x - √y)(√x + √y) + √x (√x - √y)/(√x + √y)(√x + √y)
= (√xy + y)/(x - y) + (x - √xy)/(x - y)
= (x + y) / (x - y)


2.
1/(x^2 - 1) - 2/(x+1)^2
= 1/(x + 1)(x - 1) - 2/(x + 1)^2
= (x + 1) - 2(x - 1) / (x - 1)(x + 1)^2
= (3 - x) / (x - 1)(x + 1)^2


3.
(1/x - 1/y) / (1/x^2 - 1/y^2)
= [(y - x)/xy] / [(y^2 - x^2)/(xy)^2]
= (y - x)(xy)^2 / (xy)(y + x)(y - x)
= xy / (y + x)