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Partial Fraction Expansion

  1. Sep 9, 2012 #1
    For PFE, can a denominator variables with coefficient of something other than 1, or does it have to be 1?

    For Example, can I have a term A/(3x+9)?

    It's been years since I've dealt with this and don't quite remember if this was a rule or not.

    Thanks!

    EDIT: This is in terms of taking the inverse laplace transform later.
     
    Last edited: Sep 9, 2012
  2. jcsd
  3. Sep 9, 2012 #2
    Just to put things into perspective, is the first image ok or do I have to follow what I did in the second image?
     

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  4. Sep 9, 2012 #3

    SammyS

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    You can do it either way. But why would you not factor out the 3?

    attachment.php?attachmentid=50620&d=1347238675.png

    attachment.php?attachmentid=50621&d=1347238675.png
     
  5. Sep 9, 2012 #4
    It's just been a while since I've done these. For some reason I thought it was a rule that the coefficients had to be 1 or something.

    In my 2nd image, is it set up correctly? Where the 3 remains on the left but the K1/s should not be K1/3s?
     
  6. Sep 9, 2012 #5

    SammyS

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    Oh, I missed that.

    To find the coefficients the second way, you should include the 1/3 as follows.
    [itex]\displaystyle \frac{5}{s(3s^2+30s+63)}=
    \frac{1}{3}\left(\frac{k_1}{s}+\frac{k_2}{s+3}+ \frac{k_3}{s+7}\right)[/itex]​
     
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