Asked by Anonymous
How do I simplify this Complex Rational Expression?
1/x-1+1/x+1 over 1/x-1-1/x+1
1/x-1+1/x+1 over 1/x-1-1/x+1
Answers
Answered by
Steve
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?
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?