Hi, i have attempted to solve the following:

L^-1: 3/(4s^2-9)

and got

(1/8)sinh(3t/2).

I first moved a (1/4) outside of the laplace in order to get the bottom closer to the laplace of sinh(kt) = k/(s^2-k^2). I then pulled a (1/2) out to get the 3 on the top to be 3/2 so that it would fit the equation. Is this correct? Thanks for any help!