[edit] ignore the bit about the product rule in the title [edit]

Hi everyone, this is my first time posting here I hope you guys can help me.

I am trying to get the derivative of x^2 - xy + y^2 = 3

After the first step I got:

2x - y - x(dy/dx) + 2y(dy/dx) = 0

When I get to the step where I would move all like terms to one side, I could either move all non(dy/dx) terms to the right hand side and have the equation

-x(dy/dx) + 2y(dy/dx) = y - 2x

OR if I were to move the (dy/dx) terms to the right hand side I would get:

2x - y = x(dy/dx) - 2y(dy/dx)

The first route will give me the derivative (y - 2x)/(2y - x)

The second route will give me derivative (2x - y)/(x - 2y)

It seems like I attacked both possible routes correctly, but I'm pretty sure one of the final derivatives is incorrect because (y - 2x)/(2y - x) does not equal (2x - y)/(x - 2y).... or do they?

feedback would be much appreciated!!