I have this practice problem and we were told to find the derivative of

$\displaystyle f(x)=\frac{x}{x^2+1}$

which is $\displaystyle f\prime(x)=\frac{1-x^2}{(x^2+1)^2}$

We didn't have to find the second derivative but our text gave us the answer to it.

$\displaystyle f\prime\prime(x)=\frac{(x^2+1)^2(-2x)-(1-x^2)(2)(1+x^2)(2x)}{(x^2+1)^4}=\frac{(2x)(x^2-3)}{(x^2+1)^3}$

So my question is what cancels out in the numerator to arrive at the answer. It's something so elementary but I can't seem to get my answer to match the final answer.