Find dy/dx

$\displaystyle y^2=\frac{x-1}{x=1}$

I got $\displaystyle \frac{4y}{x^2+x+1}$

The answer is $\displaystyle \frac{1}{y(x+1)^2}$

I believe I messed up with the fraction over a number, as in (what is the LaTex for this? It's not in the tutorial) 2/x^2+x+1/2y. I don't know how to deal with this. For some reason, perhaps a habit, I want to bring 2y to the top and multiply it by 2. After seeing the answer, I think it's the top times $\displaystyle \frac{1}{2y}$.

What is it? and if I'm right about the mistake? How come you do that?