Final answer:
The rational function f(x)=(x-1) / (x² +3)(x² +2) does not have any vertical asymptotes.
Step-by-step explanation:
The vertical asymptotes of a rational function occur at values of x that make the denominator equal to zero. In this case, the denominator of the function f(x) = (x-1) / (x² +3)(x² +2) is (x² +3)(x² +2). We need to find the values of x that make this denominator equal to zero. Equating the denominator to zero gives us two equations: x² + 3 = 0 and x² + 2 = 0. Solving these equations, we find that x = ±√(-3) and x = ±√(-2), respectively. Since the square root of a negative number is not a real number, there are no vertical asymptotes for this rational function.