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Math Help - partial fraction decomposition

  1. #1
    Junior Member
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    partial fraction decomposition

    Hi

    can someone help me with the following partial fraction decomposition. It is important that the answer has no complex number.

    <br />
\frac{4}{s^{2}(s^{2}+1)} = \frac{A}{s^{2}} + \frac{B}{s^{2}+1}<br />
    is
    <br />
A(s^{2}+1) + Bs^{2} = 4<br />
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  2. #2
    Senior Member
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    Remember that when a factor has a multiplicity greater than one, you should list that factor along with all its powers. In other words, since s^2 = s \cdot s, we should have factors of s and s^2.

    Also, since s^2+1 cannot be factored any further, but has degree 2, we need to use two constants in the numerator for that term.

    The whole thing should look like this:

    \frac{4}{s^{2}(s^{2}+1)} = \frac{A}{s} + \frac{B}{s^2} + \frac{Cs+D}{s^2+1}

    By the way, a good check to make sure you didn't forget any terms is to make sure the number of constants you have should equal the degree of the original denominator.
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  3. #3
    Junior Member
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    Allright thanks.

    <br />
4 = As(s^{2}+1) + B(s^{2}+1) + (Cs+D)s^{2}<br />
    4 = A + B
    0 = A
    0 = B + D
    0 = A + C

    so
    A=0, B=4, D=-4 and C=0

    which seems to be correct.
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