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Homework Help: Partial Fraction help needed

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data

    I want to decompose this (s+2)*(s+1)/(s+2)*(s+1)*(s^2+1)-1 using partial fractions so after that i can inverse Laplace it. I have been working on it for several hours but i cannot find a solution. Any help?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 5, 2008 #2
    Use parentheses so that it is clear what the expression, in particular what the denominator, is. Is it: (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)] - 1? Presumably not, as trivially (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)] - 1 = 1/(s^2+1) - 1.
    Last edited: Dec 5, 2008
  4. Dec 5, 2008 #3
    The fraction is: (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1]

    The -1 is a part of the denominator
  5. Dec 5, 2008 #4
    Thanks for clarifying, rforrevenge. The denominator (s+2)*(s+1)*(s^2+1)-1 doesn't appear to factorise, so no partial fraction decomposition is possible. Check your work up to arriving at, presumably, Y(s) = (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1]. Perhaps show us how you arrived at it.
  6. Dec 5, 2008 #5


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    Are you sure you've copied down the correct expression? The denominator expands to s^4+3s^3+3s^2+3s+1 which has no real roots/factors.
  7. Dec 5, 2008 #6
    Yes i am sure.I found out that the denominator has no roots,so there must be some problem with that expression our prof. gave us
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