Need help with partial fraction decomposition for inverse Laplace?

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Homework Help Overview

The discussion revolves around the decomposition of a rational expression involving a polynomial in the context of inverse Laplace transforms. The original poster seeks assistance with partial fraction decomposition for the expression (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1].

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are clarifying the structure of the expression, particularly the placement of parentheses and the role of the -1 in the denominator. There are questions about the correctness of the expression and its factorization properties.

Discussion Status

Some participants have provided clarifications regarding the expression's structure and have noted potential issues with the factorization of the denominator. There is an ongoing exploration of whether the original expression is accurate and what implications that has for the possibility of partial fraction decomposition.

Contextual Notes

There is uncertainty regarding the correctness of the expression provided by the professor, as participants note that the denominator does not appear to have real roots or factors, which complicates the decomposition process.

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Homework Statement



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?


Homework Equations





The Attempt at a Solution

 
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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:
The fraction is: (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1]

The -1 is a part of the denominator
 
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.
 
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.
 
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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