Quick way to do this?

Hi,

I got the below problem on practice test 2 in the GMAT Test prep softwarre.

I know you can plug in numbers and solve them, but is there a quick way to finding the answer to this?

Any insights would be appreciated.

If x and y are positive, which of the following must be greater than 1/(root x+y)?

I. (root x+y) / 2x
II. (root x) + (root y) / (x+y)
III. (root x) - (root y) / (x+y)

THank you sooo very much.

Karen