Question

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

Answer 1

The answer is `=-2/(s+2)+(2s-9)/(s^2+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)`
`=(A(s^2+9)+(Bs+C)(s+2))/((s+2)(s^2+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)`