How do I simplify this Complex Rational Expression?

Question

1/x-1+1/x+1 over 1/x-1-1/x+1

Answer 1

I assume you really meant

1/(x-1)+1/(x+1)
------------------
1/(x-1)-1/(x+1)

cross-multiply to put top and bottom over a common denominator of (x-1)(x+1)

Then since the same denominator occurs top and bottom, it can be discarded, just as

(2/3)/(5/3) = 2/5

now you have

(x+1)+(x-1)
----------------
(x+1)-(x-1)

and that's just too easy, right?