Laplace transform of (e^-s) / [ (s)(s-3) ]

[foo9008]

Homework Statement

find the laplace transform of (e^-s) / [ (s)(s-3) ]

since there's (e^-s) which can be found in L { f(t-a) H(t-a) } = (e^-(as)) F(s) , so , i found a = 1 , then i found F(s) = 1/ [ (s)(s-3) ] , formula :

i have attached the working below , is it correct ? btw , the author's ans doesn't have H(t-a) , is the author's ans wrong ?
author's ans :

Homework Equations

The Attempt at a Solution

my working :

which is correct ? the author ? or me ?

 

[Ray Vickson]

Homework Statement

find the laplace transform of (e^-s) / [ (s)(s-3) ]

since there's (e^-s) which can be found in L { f(t-a) H(t-a) } = (e^-(as)) F(s) , so , i found a = 1 , then i found F(s) = 1/ [ (s)(s-3) ] , formula :

i have attached the working below , is it correct ? btw , the author's ans doesn't have H(t-a) , is the author's ans wrong ?
author's ans :

Homework Equations

The Attempt at a Solution

my working :

which is correct ? the author ? or me ?

There is no way that an author would have asked you to find the Laplace transform of $e^{-s}/(s(s-3))$. Are you sure it does not ask for the INVERSE Laplace transform? There is a huge difference between these two concepts.