Where does f(x) = (x squared - 9) divided by (x squared - 2x - 3) have a hole rather than an asymptote?

1. Factor top and bottom before deciding what each zero of the denominator does. 2. The numerator factors as (x - 3) times (x + 3). 3. The denominator factors as (x - 3) times (x + 1). 4. The factor (x - 3) is shared by both, so its zero marks a removable discontinuity. 5. Setting x - 3 to zero gives x equal to 3, which is where the hole sits. 6. The factor (x + 1) appears only in the denominator, so x equal to negative 1 is a vertical asymptote. 7. Answering x = -3 uses a numerator factor that never appears in the denominator, so it gives an x-intercept. 8. Answering x = -1 names the asymptote rather than the hole. 9. Answering x = 0 confuses the y-intercept with a discontinuity. _Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_