Finding partial fraction expansions

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Homework Help Overview

The problem involves finding the partial fraction expansions of the polynomial expression 10/[(s^2)(s^2+6s+10)].

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to express the polynomial in a specific partial fraction form but expresses uncertainty about determining one of the coefficients. Some participants confirm the proposed form is correct and suggest methods to derive the coefficients.

Discussion Status

Participants are actively discussing the relationships between the coefficients and the implications of selecting specific values for the variable to generate equations. There is acknowledgment of the original poster's approach, and some guidance has been provided regarding the process of finding the coefficients.

Contextual Notes

There is an indication that certain values of s should be chosen to derive equations for the unknown coefficients, and the discussion hints at relationships between these coefficients that may influence the expansion process.

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Homework Statement



3. Find the partial fraction expansions of the following polynomials


a) 10/[(s^2)(s^2+6s+10)]


The Attempt at a Solution


I assume i should expan the polynomial in the form A/s^2+B/s+(Cs+D)/(s^2+6s+10) but i stuck at finding B. Maybe my expansion is just wrong .. :(
 
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The form of the expansion is correct. It should work.
 
The main idea is that the equation
\frac{A}{s^2} + \frac{B}{s} + \frac{Cs + D}{s^2 + 6s + 10} = \frac{10}{s^2(s^2 + 6s + 10)}
has to be true for any value of s except those that make one or more denominators vanish. If you pick four values of s you should get four equations in four unknowns, from which you should be able to get A, B, C, and D.
 
Have found C?

C and B are related ...
 
got it. thanks all
 

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