Using implicit differentiation with a fraction How do I solve this? What steps?  I have been beating my head into the wall all evening. 
$$ x^2 + y^2 = \frac{x}{y} + 4 $$

We have:
$$ \frac{d(x^2)}{dx} + \frac{d(y^2)}{dy}\cdot \frac{dy}{dx} = \frac{d( \frac{x}{y})}{dx} + \frac{d(4)}{dx}$$
$$2x+2y\frac{dy}{dx} = \frac{y-x \frac{dy}{dx} }{ y^2} +0$$
Can you finish?

Okay, to finish it up:
$$2y\frac{dy}{dx} - \frac{y-x \frac{dy}{dx} }{ y^2} = -2x  $$
Multiplying both sides by $y^2$
$$2y^3\frac{dy}{dx}-(y-x\frac{dy}{dx})=-2xy^2$$
$$2y^3\frac{dy}{dx}+x\frac{dy}{dx}=-2xy^2 +y$$
$$\frac{dy}{dx} \cdot (2y^3+x) =-2xy^2 +y$$
$$\frac{dy}{dx} = \frac{-2xy^2 +y}{2y^3+x}$$
