I tried working out problem c, I managed to do it mostly right but I took a few peeks at the answer sheet.

There is one part that I don't understand:

So inside the circled part, it seems they canceled the $\displaystyle \frac{(x-2)}{}$ on the top with the $\displaystyle \frac{}{(2-x)}$ on the bottom.

I don't understand exactly how they went from the (inside the blue circle) part on the left to the part on the right, can anyone explain?

Also I don't understand why there it was $\displaystyle \frac{}{(2+x)}$ on the left side, then suddenly a negative sign in front of it $\displaystyle \frac{}{-(2+x)}$ after they canceled the $\displaystyle \frac{(x-2)}{}$ and $\displaystyle \frac{}{(2-x)}$.