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Homework Help: Partial fraction decomposition

  1. Mar 21, 2006 #1

    dnt

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    can someone help me set up this problem. it asks for the partial fraction decomposition of:

    (7x^3 - 2)/[(x^2)(x+1)^3]

    i thought you put A/x^2 + B/(x+1)^3 and solve but it doesnt work that way.
     
  2. jcsd
  3. Mar 21, 2006 #2

    TD

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    It's not that simple: when your factors in the denominator are raised to a power n, you need n instances of that factor in your decomposition proposal (one for each exponent, 1 -> n). In your case:

    [tex]
    \frac{{7x^3 - 2}}{{x^2 \left( {x + 1} \right)^3 }} = \frac{A}{{x^2 }} + \frac{B}{x} + \frac{C}{{\left( {x + 1} \right)^3 }} + \frac{D}{{\left( {x + 1} \right)^2 }} + \frac{E}{{x + 1}}
    [/tex]

    Do you get the idea?
     
  4. Mar 21, 2006 #3

    dnt

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    yeah that makes sense. is there another way to do it where you put Ax+B over the x^2 and Cx^2 + Dx + E over the (x+1)^3 and do it with just two fractions?
     
  5. Mar 21, 2006 #4

    TD

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    Sure, since (my A and B are the other way arround though)

    [tex]\frac{A}{{x^2 }} + \frac{B}{x} = \frac{A}{{x^2 }} + \frac{{Bx}}{{x^2 }} = \frac{{A + Bx}}{{x^2 }}[/tex]

    I don't see how this would make any significant difference though...
     
  6. Mar 21, 2006 #5

    dnt

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    ok cool - im sure it wouldnt but i just wanted to be sure.
     
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