Your notation is terrible. x represents the function in the time domain. You just cannot use the same symbol to represent the Laplace transform of x.

And you donothave the answer as s + 4/s(s-2). Wherever you're getting the answer from will say , which you should have written as (s+4)/s(s-2) if you're not going to typset your equations. s + 4/s(s-2) doesnotmean , it means .

Let LT(x) = X.

Then, using basic algebra (which you're expected be competent in if you're studying at a level that includes Laplace transforms):

etc.