Consider the function $f(x) = \frac{x^2 - 4}{x(x - 2)}$.
a. Evaluate $\lim_{x \to \infty} f(x)$ and $\lim_{x \to -\infty} f(x)$, and then identify the horizontal asymptotes.
b. Find the vertical asymptotes. For each vertical asymptote $x = a$, evaluate $\lim_{x \to a^-} f(x)$ and $\lim_{x \to a^+} f(x)$.
a. Evaluate $\lim_{x \to \infty} f(x)$. Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. $\lim_{x \to \infty} \frac{x^2 - 4}{x(x - 2)} = $ (Simplify your answer.)
B. The limit does not exist and is neither $-\infty$ nor $\infty$.