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Partial Fraction Decomposition

  1. May 11, 2008 #1
    1. The problem statement, all variables and given/known data
    I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc.

    [e^(-2s) / (s^2+1)(s-1)(s+1)^2]

    2. Relevant equations

    3. The attempt at a solution

    I'm not quite sure how to work with the e^-2s, but as far as doing the partial fractions, is this right: ?

    Ax+B/(s^2+1) + C/(s-1) + D/(s+1) + E/(s+1)

    I really just need help with that first step, making sure I set it up right, and also on how to deal with the e^(-2s). Do I take it out and treat it as 1? Do I set what I get from the partial fraction decomposition equal to e^(-2s) or something else??

    Thanks!
     
  2. jcsd
  3. May 11, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The last one should be E/(s+1)^2.

    No, you do not treat e^(-2s) as 1- it isn't!
    You write
    [tex]\frac{e^{-2s}}{(s^2+1)(s-1)(s+1)^2}= \frac{As+B}{s^2+1}+ \frac{C}{s-1}+ \frac{D}{s+1}+ E/(s+1)^2[/itex]
    for all x and solve for A, B, C, D, E.

    Probably the simplest way is to multiply both sides by [itex](s^2+ 1)(s- 1)(s+1)^2[/itex] to get rid of the fractions, then take s equal to whatever 5 numbers you wish so you get 5 equations to solve.
     
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