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Really Simple!

  1. Nov 30, 2007 #1
    How do I simplify this?

    [tex] \frac{1}{x-2} - \frac{1}{x^2-4} = \frac{(x^2-4)-(x-2)}{(x^2-4)(x-2)}[/tex]
     
  2. jcsd
  3. Nov 30, 2007 #2

    Dick

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    Combine the 4 and 2 in the numerator so you have a single quadratic. Then see if it factors so you can see of if there are any common factors you can cancel.
     
  4. Nov 30, 2007 #3
    [tex] \frac{x^2-x-2}{(x^2-4)(x-2)} [/tex]

    I know I should be able to see this instantly but I'm not! What comes next?
     
  5. Nov 30, 2007 #4

    Dick

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    You don't have to see it instantly. Can you factor the numerator?
     
  6. Nov 30, 2007 #5
    Like this?

    [tex] \frac{x^2-x-2}{(x-2)(x+2)(x-2)} [/tex]
     
    Last edited: Nov 30, 2007
  7. Nov 30, 2007 #6
    [tex] \frac{x^2-x-2}{(x-2)^2(x+2)} = \frac{x+1}{(x-2)(x+2)}[/tex]

    The final step is the answer but I don't know how to get there. What are the rules here?
     
  8. Nov 30, 2007 #7

    after this stage

    factor the numerator

    x2 - x - 2 = (x-2)(x+1)

    right?

    then u can cancel t he (x-2) in the numerator and denominator and ur left with that answer that ur looking for
     
  9. Nov 30, 2007 #8
    I'm having one of those dumb days right know. Jesus!

    Thank you Dick and salman213.
     
  10. Nov 30, 2007 #9

    HallsofIvy

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    They said factor the numerator! (Although factoring the denominator doesn't hurt.)
     
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