
The question require me to find the inverse of Laplace transform. In the first line of solution, how does it go from LHS to RHS? Does it simply apply partial fractions?

The question require me to find the inverse of Laplace transform. In the first line of solution, how does it go from LHS to RHS? Does it simply apply partial fractions?
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hint: $s^2 = \dfrac{2s^2}{2} = \dfrac{1}{2}\left((s^2-4)+(s^2+4)\right)$