I've had problems with this for a while now...can someone please explain?
There are a number of ways you can distribute a negative over a rational expression. Here are a few of them.
$\displaystyle -\left(\frac{x^3-3}{x^2+1}\right)=\frac{-(x^3-3)}{x^2+1}=\frac{-x^3+3}{x^2+1}=\frac{3-x^3}{x^2+1}$
$\displaystyle -\left(\frac{x^3-3}{x^2+1}\right)=\frac{x^3-3}{-(x^2+1)}=\frac{x^3-3}{-x^2-1}$