Consider the rational function $R(x) = \frac{x^2 - 4}{x^2 - x - 6}$. Which of the following accurately describes the discontinuities of $R$?

Core Concept

Factoring the numerator and denominator yields $R(x) = \frac{(x-2)(x+2)}{(x-3)(x+2)}$. The common factor $(x+2)$ creates a hole at $x = -2$, and the remaining factor $(x-3)$ in the denominator creates a vertical asymptote at $x = 3$.