In an ideal world, people would leave lazy guys like me in peace, but you make me do the calculations

Here they are:

Subtracting (1) from stem, we get

1/√(x+y) - √(x+y)/2x

= (2x - x - y)/[2x√(x+y)]

= (x - y)/[2x√(x+y)]

We don't know relative values of x and y, hence can't say if (1) is greater than stem, as we can't say whether the expression is +ve or -ve.

Subtracting (2) from stem, we can definitely say that (2) is greater than stem, as mendiratta has explained.

Subtracting (3) from stem, we get

1/√(x+y) - (√x-√y)/(x+y)

= [√(x+y) - √x + √y]/(x + y)

This is always +ve, which means the stem is always larger than (3).

So answer is (2) <phew>!