asymptote is at x = 3, then x - 3 is a factor of the denominator, and no other such linear (neatly solveable in the whole numbers) factor exists there.
If the function has an horizontal asymptote that is off the x-axis, then the degree of the numerator is the same as the degree of the denominator.
The simplest conclusion would then be that the rational function is of the form f(x) = (2x + b)/(x - 3), where "b" is some constant.
We are given that f(1.5) = 0, so (3 + b)/(1.5 - 3) = 0. A fraction is zero only when its numerator is zero, so 3 + b = 0.
What then is the value of "b"?