Separating a fraction

Discussion in 'Math' started by boks, Dec 1, 2008.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    I don't remember what this method is named in English, but I want to write the fraction

    \frac{1}{(s^2 + 1)(s-3)(s+2)}

    in the form

    \frac{A}{s^2 + 1} + \frac{B}{s-3} + \frac{C}{s+2}

    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

    As^2 - As - 6A + Bs^3 + 2Bs^2 + Bs + 2B + Cs^3 - 3Cs^2 + Cs - 3C = 1

    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...
     
  2. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    You have to put As+D over (s^2+1) and not just A.
     
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    OK, thanks. What is the method called? I'm trying to find something on the internet.
     
  4. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    The general is partial fractions, I think this is called partial fractions with repeated and quadratic roots.
     
  5. blazedaces

    Active Member

    Jul 24, 2008
    130
    0
    It's also called partial fraction expansion.
    Good luck,
    -blazed
     
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