I was doing an exercise and ran into a problem with their use of factoring. Here is the problem specific to where the issue occurs:
$ \frac{(x^2 + 1)^{1/2} - x^2 (x^2 + 1)^{-1/2}}{x^2 + 1} = \frac{(x^2 + 1)^{-1/2}\left( x^2 + 1 - x^2\right)}{x^2 + 1} $
If $(x^2+1)^{-1/2}$ was factored out on the top, shouldn't the amount after factoring be just be $1 - x^2$? I am not seeing where the extra $x^2$ is coming from. Can anyone spot the issue I am having?