As part of trying to solve a differential equation using Laplace transforms, I have the fraction $\frac{-10s}{(s^2+2)(s^2+1)}$ which I am trying to perform partial fraction decomposition on so that I can do a inverse Laplace transform. When I try to work out this fraction, I get that $-10=0(A+B)$ since $s^1$ does not show up in the fraction. How does partial fraction decomposition work for a fraction like this?


I think you should work on the following, instead:


Or use the convolution theorem.

  • $\begingroup$ Thank you, I can't believe I forgot about that. It's been about a year since I last did partial fractions. $\endgroup$ – Chris Crutchfield Mar 6 '15 at 3:28
  • $\begingroup$ @ChrisCrutchfield: Thanks! I am I could help you. :-) $\endgroup$ – mrs Mar 6 '15 at 6:24










imply $A=10$, $B=0$, $C=-10$ and $D=0$.


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