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Math Help - Partial Fraction Decomposition

  1. #1
    Junior Member
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    Sep 2008
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    Canada
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    Partial Fraction Decomposition

    Hi everyone!
    I need a helping hand here with factoring this denominator:

    \frac {-5x + 15}{x^2 + 2x - 63}

    I feel a bit stupid, can I use completing the square? Or do I need to use the quadratic formula? If I complete the square I think I got...

    (x-1)^2 - 64

    I don't know, rather confused.
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  2. #2
    Newbie
    Joined
    Apr 2009
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    Response

    Remember how to factor something like x^2-5x+6?
    Remember the middle term (-5x) is the sum of the product of the coefficient of the first and last term. So in this case the only numbers that would add up to -5 (coefficient of middle term) and whose product would be +6 would be -3 and -2. So from here, you could expand the expression as x^2-3x-2x+6   -> x(x-3)-2(x-3)= (x-2)(x-3)
    There should be a common factor in both pars (x-3). I do not want to give you the answer (sorry!). Hopefully, this will trigger your memory.
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  3. #3
    Junior Member
    Joined
    Sep 2008
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    Canada
    Posts
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    Hohoho, I'm so bad at basic math.
    Yeah you're right, so it's...

     (x+9) (x-7)
    Thank you!
    bahahah....
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