Partial Fraction Decomposition

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SUMMARY

The discussion centers on the partial fraction decomposition of the rational function (22x^2 + 60x + 58) / ((s + 1)(x^2 + 4x + 5)^2). The user has calculated the coefficients A, B, C, D, and E as 5, -1777/29, -6143/29, -570/29, and 840/29, respectively. To verify these values, the user suggests setting up equations with the partially fractioned version on the right and the original function on the left, simplifying to check if the numerators match.

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  • Understanding of partial fraction decomposition
  • Familiarity with polynomial long division
  • Knowledge of algebraic manipulation techniques
  • Basic calculus concepts for function analysis
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  • Review the method of partial fraction decomposition in detail
  • Practice polynomial long division with various rational functions
  • Explore algebraic manipulation techniques for simplifying expressions
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Students in algebra, mathematicians, and anyone studying calculus or advanced algebra who need to understand or verify partial fraction decomposition techniques.

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Hey eveyone,

trying to determine the partial fraction decomposition of:

(22x^2+60x+58)
(s+1)(x^2+4x+5)^2

I got values for my unknowns A, B, C, D,E are:
A=5
B=-1777/29
C=-6143/29
D=-570/29
E=840/29

If anyone out there can double check these for me.
 
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A self check with partial fractions is fairly easy. Set up the two equations with the partially fractioned version on the right and the original on the left and simplify the right side. See if the numerator turns out to be the same.
 

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