Now, this is a weird question, because the answer is more complicated to evaluate than the original question. However, it appears they want you to rationalize the denominator.
sqrt(x)
----------
3*sqrt(x) - sqrt(y)
Multiply top and bottom by the conjugate:
x^{1/2}(3x^{1/2} + y^{1/2})
----------------------
(3x^{1/2} - y^{1/2})(3x^{1/2} + y^{1/2})
3x + x^{1/2}y^{1/2}
-----------------
9x + 3x^{1/2}y^{1/2} - 3x^{1/2}y^{1/2} - y
3x + x^{1/2}y^{1/2}
−−−−−−−−−−−−
9x - y
Let's try it out for x = 16 and y = 9
Original:
16^(1/2)
-----------
3(4) - 3
4/9
New:
3(16) + 16^(1/2) 9^(1/2)
----------------------
9(16) - 9
48 + (4)(3)
------------
144 - 9
60/135 = 4/9