[ (-s^2) -3s +27 ] / [ (2(s^2) + 18s +2 ] = I(s)

 

I guess you need to get i(t)...
Well, I guess you can write:
I(s) = -0.5{ [ (s^2) +3s - 27 ] / [ s^2 + 9s +1 ] }
then simply say that: -2I(s) = A + [(Bs + C) / (s^2 + 9s +1)]
Then from coefficient equalization you get A, B and C.
"Plug" them into the equation, and from there it's easy enough to find i(t).


Correct me if I'm wrong though.

 

I'm almost 100% sure that you can't operate the way it is because the numerator must be (<) but never (>) or equal to the denominator. You have to perform polynomial division to make the numerator smaller than denominator, I'm speaking of exponents or powers of course(both terms are s^2). This is an improper fraction in other words