Question

i have a question about partial fraction expansion , ok so given 1/s(2s^2 +10) how would you set up the partial fraction? i wanna compare my answer to yours

Answer 1

`\frac1{s(2s^2+10)}=\frac{a_1}s+(a_2s+a_3)/(2s^2+10)`

`1=a_1(2s^2+10}+(a_2s+a_3)s`

`1=(2a_1+a_2)s^2+a_3s+10a_1`


`\implies\begin{cases}2a_1+a_2=0\\a_3=0\\10a_1=1\end{cases}\implies a_1=\frac1{10},a_2=-\frac15,a_3=0`


`\implies\frac1{s(2s^2+10)}=\frac1{10s}-\frac s{5(2s^2+10)}`

`\frac1{s(2s^2+10)}=\frac1{10s}+\frac s{10(s^2+5)}`