Rationalize the denominator. Hm.
You know how something like (x+1)(x-1) makes x^2 - 1 with no x term in the middle? Like that.
multiply the top and bottom by x-2Sqrt(y)
4( Sqrt(x) )(x - 2Sqrt(y) ) / (x + 2Sqrt(y) )(x - 2Sqrt(y) )
multiply the bottom parts together
4( Sqrt(x) )(x - 2Sqrt(y) ) / (x^2 - 4y)
if you want, multiply the tops together too
4(x^3/2 - 2Sqrt(xy) ) / (x^2 - 4y)
or even
(4x^3/2 - 8Sqrt(xy) ) / (x^2 - 4y)