Okay, so it might be a little difficult to explain it but here we go:
You find the LCD (lowest common denominator) and multiply the top and bottom half of the fraction by the LCD:
(1/x) times xy (since it is divisible by both x and y)
then you do the same for the bottom (2/y) times xy
The x's on the top cancel out leaving you with 1/y
The y's on the bottom cancel out leaving you with 2/x
So now you multiple the top half (numerator) by the reciprocal of the denominator. In other words, multiply (1/y) by (x/2).
The answer is x/2y