Simplify this expression. Assume that all variables are positive.
X2/3y-1/4
---------------
x1/2y-1/2
for X, 2/3 is bigger than 1/2, so that 1/2 should go up to be subtracted from 2/3,
but for Y, 1/2 is bigger than 1/4, so that 1/4 should go down to be subtracted from 1/2.
with the X's on top and the Y's on the bottom you get.
X2/3-1/2
_______
Y1/2-1/4
hopefully you recall how to find common denomiators for the top.
2/3 - 1/2
4/6 - 3/6 = 1/6
logic will tell you if you have half and subtract a quarter, a quarter remains,
if not then do the common demoniators again
X1/6
_______
Y1/4
for X, 2/3 is bigger than 1/2, so that 1/2 should go up to be subtracted from 2/3,
but for Y, 1/2 is bigger than 1/4, so that 1/4 should go down to be subtracted from 1/2.
with the X's on top and the Y's on the bottom you get.
X2/3-1/2
_______
Y1/2-1/4
hopefully you recall how to find common denomiators for the top.
2/3 - 1/2
4/6 - 3/6 = 1/6
logic will tell you if you have half and subtract a quarter, a quarter remains,
if not then do the common demoniators again
X1/6
_______
Y1/4