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?
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