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Laplace transformations

  1. Dec 1, 2008 #1
    Separating a fraction

    I don't remember what this method is named in English, but I want to write the fraction

    [tex]\frac{1}{(s^2 + 1)(s-3)(s+2)}[/tex]

    in the form

    [tex]\frac{A}{s^2 + 1} + \frac{B}{s-3} + \frac{C}{s+2}[/tex]

    I multiply A with (s-3)(s+2), B with (s^2 + 1)(s+2) and C with (s^2 + 1)(s-3), to get

    [tex]As^2 - As - 6A + Bs^3 + 2Bs^2 + Bs + 2B + Cs^3 - 3Cs^2 + Cs - 3C = 1[/tex]

    and the equations

    (1) B + C = 0
    (2) A + 2B - 3C = 0
    (3) -A + B + C = 0
    (4) -6A + 2B - 3C = 1

    (1) and (3) gives A = 0
    (2) then gives B = C = 0

    This is obviously wrong. The correct answer is

    A = 2s - 4
    B = 2
    C = -4

    according to my book. There must be something I don't understand here...
     
    Last edited: Dec 1, 2008
  2. jcsd
  3. Dec 1, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    For the fraction containing the denominator of (s^2+1), the numerator should be As+B.
     
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