Simplifying Rational Expressions

I'm doing my victory lap (Grade 13), and I need a credit in Advanced Functions.

I'm already working my butt off to keep up with the review, but I feel that I need a solid foundation of these concepts before I can really excel in this course. So, If anybody could give me a hand...

I looked at (x^2 - 1) as a difference of squares, and then multiplied each side by the other's denominator to achieve a common denominator.

http://img367.imageshack.us/img367/5...ession2wk1.jpg

Then I canceled, and ended up with this:

http://img238.imageshack.us/img238/1...ession3hy2.jpg

Collected like terms...

http://img74.imageshack.us/img74/937...ession4cs7.jpg

Then, I thought - I'm way off track here. The answer is apparently

http://img139.imageshack.us/img139/7...ession5db3.jpg

I'm hoping someone can do the answer, and explain to me where I went wrong. I've tried it several times, but I'm just too rusty, I think. Thanks a million to whoever's up to the task!

- Cameron