(x^4*y^4 - x^2*y^2)/(x^3*y^2)
I'm not sure where you got 3y^2 / 2y^2, but I don't see that you can get that from this.
If we break up the fraction, we get
(x^4*y^4)/(x^3*y^2) - (x^2*y^2)/(x^3*y^2) = x*y^2 - 1/x
Maybe I'm misunderstanding the problem.