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Find $\mathcal{L}^{-1}\left(F(s)\right)$ if:

$$\displaystyle F(s) = \frac{1}{s^2-4}$$

A

$$ e^{2t} - e^{-2t}$$

B

$$\frac{3}{4} e^{2t} -\frac{1}{4} e^{-2t}$$

C

$$\frac{1}{4} e^{2t} -\frac{1}{4} e^{-2t}t$$

D

$$\frac{1}{3} e^{2t} -\frac{1}{5} e^{-2t}$$

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