You are so close.
the book gives me
Laplace impedance for a capacitor is Z=V/I=1/Cs
what is the Laplace impedance for an inductor? Z=Ls?
so would Vout=(Zc/R+Zc+ZL)Ein
(1/Cs)/(R+Ls+(1/Cs)) (This expression is correct)
1/RCs+LCs for an answer (for some reason you made an error in your simplification process)
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