Differentiating $y^2 - \frac{y}{x-1}=4$ I am attempting to differentiate this function, but I am not having success in getting rid of fractions so that I can separate $\frac{dy}{dx}$ onto one side of the question. These are the steps I have followed:
Step 1
$$2y\frac{dy}{dx}-\frac{(x-1)\frac{dy}{dx}-y}{(x-1)^2}=0$$
Step 2
$$\frac{(x-1)^2(2y)\frac{dy}{dx}-(x-1)\frac{dy}{dx}-y}{(x-1)^2}=0$$
I am unsure of where to go from here. Any advice would be greatly appreciated.

$$(x-1)^2(2y)\frac{dy}{dx}-(x-1)\frac{dy}{dx}-y=0$$
$$(x-1)^2(2y)\frac{dy}{dx}-(x-1)\frac{dy}{dx}=y$$
$$\left[2y(x-1)^2-x+1\right]\frac{dy}{dx}=y$$
$$\frac{dy}{dx}=\frac{y}{2y(x-1)^2-x+1}$$
