how do I solve this problem?

X^2=(X-Y)/(X+Y)

What exactly is the problem? To calculate dy/dx? Since you titled your thread "Calculus-implicit differentiation", I'd presume that that's it, but you didn't make it clear.

With the information given I would assume he wants Y in terms of X?

It has been a long time since I've hit this topic. I quickly looked at the following page for a refresher:
http://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation

Everyone else, please review my result and agree or disagree, my confidence in it is low especially since it is ugly!

I assumed we are trying to find dy/dx

x^2=(x-y)/(x+y)
move things around a little to make the derivative easier (for me)
x^2*(x+y)=x-y
x^3+yx^2-x+y=0
d(x^3)/dx + yd(x^2)/dx + x^2dy/dx-dx/dx+dy/dx=d0/dx
3x^2+2yx+x^2dy/dx-1+dy/dx=0
x^2dy/dx+dy/dx=1-3x^2-2yx
(dy/dx)(x^2+1)=1-3x^2-2yx
dy/dx=(1-3x^2-2yx)/(x^2+1)

What is the consensus of the group?

p.s. anyone know if there's any math markup we can use on here simply? Writing equations as plain text is obviously ugly and confusing