Find the inverse Laplace transform?

Question

Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4).

Answer: f(t)=2 cosh 2t-(3/2) sinh 2t

Answer 1

I found an alternative answer.

We can first factor (2s - 3)/(s² - 4) into A/(s+2) + B(s - 2). By the solution methods in your book, you should get A = 7/4 and B = 1/4. We know that F(s) = A/(s - a) means that f(t) = e^-at, so what you should get for the answer is f(t) = 7/4 * e^-2t + 1/4 * e^2t.