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Partial Fraction Expansion

  • Thread starter btbam91
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  • #1
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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.
 
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  • #2
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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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  • #3
SammyS
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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.
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
 
  • #4
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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?
 
  • #5
SammyS
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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?
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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