[tex]\dfrac1{s(2s^2+10)}=\dfrac{a_1}s+\dfrac{a_2s+a_3}{2s^2+10}[/tex]
[tex]1=a_1(2s^2+10}+(a_2s+a_3)s[/tex]
[tex]1=(2a_1+a_2)s^2+a_3s+10a_1[/tex]
[tex]\implies\begin{cases}2a_1+a_2=0\\a_3=0\\10a_1=1\end{cases}\implies a_1=\dfrac1{10},a_2=-\dfrac15,a_3=0[/tex]
[tex]\implies\dfrac1{s(2s^2+10)}=\dfrac1{10s}-\dfrac s{5(2s^2+10)}[/tex]
[tex]\dfrac1{s(2s^2+10)}=\dfrac1{10s}+\dfrac s{10(s^2+5)}[/tex]
