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Math Help - Partial Fraction Expansion

  1. #1
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    Partial Fraction Expansion

    Hi, this is my first post, so I apologize if it is not formatted correctly. I'm working through a laplace transform for my controls class and I'm having trouble understanding the solution to the example given in class.

    (s^3 + 3s^2 + 1)/((s^2*(s+1)*(s+2))

    Why/how does this expand to (A/s) + (B/(s^2)) + (C/(s+1)) + (D/(s+2))?

    Mainly, where does that first term (A/s) come from?


    Any help would be greatly appreciated. Thanks!
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Partial Fraction Expansion

    In general if a fraction has a repeated factor in the denominator then we split it as:
    \frac{T(x)}{(x-a)(x-b)^2}=\frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{(x-b)^2}

    Where T(x) is the numerator.
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  3. #3
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    Re: Partial Fraction Expansion

    Thank you. I appreciate it. I forgot about the repeated factor business.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Partial Fraction Expansion

    You're welcome!
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