I'm looking at my notes and one of my professors steps goes from:

$\displaystyle \frac{x}{x-1}-\frac{x}{x+1}$

to

$\displaystyle \frac{1}{x-1}+\frac{1}{x+1}$

What happened to the numerator? I know this is not a mistake because when I enter the first line into my ti-89 it spits out the second line.