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You can use the assume command:

sage: var('s t')
(s, t)
sage: f = t^(-1)*exp(-t)-t^(-1)*exp((3)*t)
sage: f.laplace(t,s)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
[...]
TypeError: ECL says: Maxima asks: Is  s-3  positive, negative, or zero?

sage: assume(s-3>0)
sage: f = t^(-1)*exp(-t)-t^(-1)*exp((3)*t)
sage: f.laplace(t,s)
log((s - 3)/(s + 1))

This mostly works, at least for simple enough conditions.