Determine the inverse Laplace transform

Question

Find the  laplace inverse transform,F(s)=2s-3/s^2+2s-3

Answer 1

F(s)=(2s-3)/[(s+3)(s-1).

Express as partial fractions: A/(s+3)+B/(s-1) where A, B are constants to be found.

A(s-1)+B(s+3)≡2s-3;

A+B=2, -A+3B=-3⇒4B=-1, B=-¼, A=2-B=9/4.

F(s)=(9/4)/(s+3)-¼/(s-1), f(t)=(9/4)e^-3t-¼e^t, or ¼(9e^-3t-e^t).