Manahattan 5lb: 8.41- Different answers from different techniques

Problem statement:
x > y
xy 0
A: x^2/(y+1/y)
B: y^2(x+1/x)

My question:
The expression was simplified to
A: x^3 + x
B: y^3 + x

In the simplified expression, A is always greater. Tested with (x,y) values (1,-1) (2,1) and (-1,-2)

However, a direct substitution of values into the expression without simplification gives one case B > A and another of A > B. This is the 5lb response as well.

5lb Response:

Your cross-multiplication step is the problem, as you cannot directly do that without having to consider for different cases.

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