How do you express (-5s-36) / [ (s+2) (s^2+9) ]−5s−36(s+2)(s2+9) in partial fractions?

1 Answer
Narad T.
Nov 5, 2016

The answer is =-2/(s+2)+(2s-9)/(s^2+9)=−2s+2+2s−9s2+9

Explanation:

Let's start the decomposition in partial fractions
(-5s-36)/((s+2)(s^2+9))=A/(s+2)+(Bs+C)/(s^2+9)−5s−36(s+2)(s2+9)=As+2+Bs+Cs2+9
=(A(s^2+9)+(Bs+C)(s+2))/((s+2)(s^2+9))=A(s2+9)+(Bs+C)(s+2)(s+2)(s2+9)

:.-5s-36=A(s^2+9)+(Bs+C)(s+2)
let s=-2=>-26=13A=>A=-2 #-36=9A+2C=>#C=-9
coeficients of s, -5=2B+C=>B=2
:.(-5s-36)/((s+2)(s^2+9))=-2/(s+2)+(2s-9)/(s^2+9)

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