How do I take the inverse laplace transform of something that looks like this? It's part of a larger piecewise-defined second order differential equation, but this is the part I'm stuck on.(adsbygoogle = window.adsbygoogle || []).push({});

(-4s-1)/(4s^2 + s + 4)

Completing the square doesn't work for the bottom, so I figure I need to separate the whole thing into two separate fractions. I still can't figure out how to take the inverse laplace of either resulting fraction, however.

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# Taking the inverse laplace of this?

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