So I've set a goal for myself to relearn all the math I once knew, one textbook at a time. Realizing I could do at age 10 what I can't do now is humbling. Anyway.

I've got this problem and can't figure out how to get the correct answer:

c^{-2 }- 1

-------

c^{-1 }+ 1

I've tried to work it as follows:

1

-- - 1

c^{2 }^{--------- 1 --- + 1 }c

Clear the fraction by multiplying by c^{2}across all numerators.

This leaves

1 - c^{2 }-------

c + c^{2}

However, my book says the answer is:

1 - c

------

c

I can't for the life of me get there.

Help?

[[EDIT:

Oh good lord. After trying for over an hour I worked backwards from the given solution and got how to simplify to the correct answer.

However, if this had been a proper exam I would've never thought to factor down to what is 'correct'. I only got there because I knew what was right.

Any tips on knowing when factoring is possible? Or quicker ways to recognize those patterns? Help would be appreciated.]]