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Help with partial fractions

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data

    I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions.

    2. Relevant equations

    So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4)

    3. The attempt at a solution

    To simplify:
    9= D(s-1)(s-4)+ E(s-1)(s-4)+ F(s-1)^2
    So since (s-1)(s-4)=s^2-5s+4
    9= Ds^2-5Ds+4D+Es^2-5Es+4E+Fs^2-2Fs+F
    So collect like terms
    9=(D+E+F)s^2+(-5D-5E-2F)s+4D+4E+F

    Now there's three equations and three terms.
    D+E+F=0, -5D-5E-2F=0 and 4D+4E+F=9

    I have come up with the following D=-1.2, E=4.2, and F=-3 using all three equations but it doesn't satisfy the second equation. I tried to solve this system with a matrix, but that didn't work. I'm wondering if a unique solution even exists...any insight is highly appreciated.
     
  2. jcsd
  3. Nov 4, 2007 #2
    right side is wrong. it should be E/(s-1)^2
     
  4. Nov 4, 2007 #3

    rock.freak667

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    Homework Helper

    (s-1)(s-1)(s-4)=(s-1)^2(s-4)

    so 9/(s-1)^2(s-4) = A/(s-1)^2 + B/(s-1) + C/(s-4)
     
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