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Easy one, probably factoring

  1. Oct 8, 2007 #1

    tony873004

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    This is a small step in a larger Calc problem. There's 2 problems in a row where this same arrangement popped up. I have a feeling I'm forgetting something basic. How does [tex]{\frac{{x^2 }}{{x^2 - 1}}}[/tex] become [tex]1 + \frac{1}{{x^2 - 1}}[/tex] ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 8, 2007 #2

    Dick

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    Use polynomial long division to divide the numerator by the denominator. This gives you quotient, 1, and a remainder, 1. Just like 5/4=1+1/4.
     
    Last edited: Oct 8, 2007
  4. Oct 8, 2007 #3
    add and subtract 1 from the numerator

    then we get


    [tex] \frac{x^2}{x^2 -1} = \frac{x^2 - 1 + 1}{x^2 -1} = \frac{x^2-1}{x^2-1} + \frac{1}{x^2 -1} = 1 + \frac{1}{x^2 + 1}[/tex]
     
  5. Oct 8, 2007 #4

    tony873004

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    2 great answers. I knew it wasn't hard, but I'd have never come up with either of these on my own. Thanks!!
     
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