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I don't understand partial fraction decomposition

  1. Jun 27, 2013 #1
    if there is something like (x^2+3x+6) in the denominator for one of the terms in a partial fraction problem, why do we put Ax+B instead of just A? and if the denominator is (x^2+3x+6)^2, why do we do {(Ax+B)/(x^2+3x+6)}+{(Cx+D)/(x^2+3x+6)^2}? i was always just told to memorize it, but why do we set it up this way? even a link to a derivation will probably help. the only thing i can find online is the formulas, basically what i just wrote.. but i want to know why those setups are the way they are, ie the reason behind them.
     
  2. jcsd
  3. Jun 27, 2013 #2

    HallsofIvy

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    Have you thought about the simplest cases? Suppose your initial fraction is just [itex](4x- 2)/(x^2+ 3x+ 6)[/itex]. Do you think you ought to be able to write that as [itex]A/(x^2+ 3x+ 6)[/itex]? What would have happened to the "4x"?
     
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