Partial Fractions: Solving 4/((s^2) + 4)(s-1)(s+3)

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SUMMARY

The discussion focuses on solving the partial fraction decomposition of the expression 4/((s^2) + 4)(s-1)(s+3). Participants confirm that the correct form for the decomposition includes a linear numerator for the quadratic denominator, specifically (As + B)/((s^2) + 4) + C/(s-1) + D/(s+3) = 4. This approach is necessary due to the nature of the quadratic term in the denominator, which requires a first-degree polynomial in the numerator.

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  • Understanding of partial fraction decomposition
  • Familiarity with polynomial functions and their degrees
  • Knowledge of algebraic manipulation techniques
  • Basic calculus concepts related to limits and integrals
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  • Practice solving similar expressions involving quadratic and linear factors
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Students studying algebra, calculus, or engineering mathematics, particularly those tackling problems involving rational functions and partial fraction decomposition.

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Homework Statement



we have 4/((s^2) + 4)(s-1)(s+3)

Homework Equations





The Attempt at a Solution



dividing it up do we get:

A/((s^2) + 4) + B/(s-1) + C/(s+3) = 4

or is it

(As + B)/((s^2) + 4) + C/(s-1) + D/(s+3) = 4
 
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The second one. Since the denominator s2+ 4 is quadratic the numerator may be As+ B.
 
cheers!
 

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