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Math simplify problem

  1. Jul 20, 2006 #1
    I have a problem where I got the final answer:

    Code (Text):

           1              1
    -  ---------   -  --------
       (u - 1)^2       (u + 1)^2
     

    which is correct, but the book further simplifies it to:

    Code (Text):

         2(1 + u^2)
    -  -------------
        (u^2 - 1)^2
     
    I tried and tried, but couldn't figure out how to simplify it to that result. Can someone please explain the process to me?

    Thanks!
     
  2. jcsd
  3. Jul 20, 2006 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you remember adding fractions from fourth grade arithmetic?

    Get a common denominator and add.

    The denominator of one fraction is (u-1)2= (u-1)(u-1) and the denominator of the other is (u+1)2[/sup= (u+1)(u+1). The "least common denominator" is (u-1)(u-1)(u+1)(u+1)= (u-1)(u+1)(u-1)(u+1)= (u2-1)(u2-1)= (u2-1)2.
    [tex]-\frac{1}{(u-1)^2}- \frac{1}{(u+1)^2}= -\frac{(u+1)^2}{(u-1)^2(u+1)^2}-\frac{(u-1)^2}{(u-1)^2(u+1)^2}[/tex]
    [tex]= -\frac{u^2+ 2u+ 1}{(u^2-1)^2}-\frac{u^2-2u+1}{(u^2-1)^2}[/tex]
    [tex]= -\frac{2u^2+ 2}{(u^2-1)^2}= -\frac{2(u^2+1)}{(u^2-1)^2}[/tex]
     
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