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I've got through most of a problem that involves finding an inverse laplace transform, but I am stuck at one part that requires algebraic manipulation. The function is

1/[s(2s^{2}+2s+1)]

So far I have modified it too look like .5/[s(s+.5)^{2}+.5^{2}](1/.5)

I'm not sure how to modify the function with that extra s in the denominator.

I had seen that the function could be transformed into (1/s) - [(s+.5)+.5]/[(s+.5)^{2}+.5^{2}and then from that the inverse Laplace could be easily obtained, but I am not sure how this transformation was done. I am sure there is a property I'm not thinking of, but any help on this would be greatly appreciated!

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# Inverse Laplace Transform

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