ignore the bit about the product rule in the title 
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!!