((x^2+1)^(1/2) - x^2(x^2-1)^(-1/2)) / (x^2-1)

The book says 1/(x^2+1)^3/2

While trying different things I figured out the rule that the square root of a divided by a = 1/ square root of a. There must a rule I could use here. My answer always has x^2 in the numerator.

Thanks!