Trouble taking a derivative

I have to take the derivative of $\displaystyle \frac{y - 1}{y^2 - y + 1}$:

http://i.imgur.com/d9DY1.png

The solution is $\displaystyle \frac{y^2 - 2y}{(y^2 - y + 1)^2}$ but in my work, the answer will have something to the 4th power on the top which will be impossible to cancel out. What have I done wrong?

Edit: Never mind, I see my mistake

Re: Trouble taking a derivative

Your differentiation is correct, but you go wrong at the third line.

$\displaystyle (y^{2} -y + 1)^{-2} = \frac{1}{(y^{2} - y + 1)^{2}},$

there shouldn't be any square roots.