1. **State the problem:** Find the zeros of the function $$g(x) = \frac{x^2 - 16}{x - 4}$$ with domain $$\mathbb{R} \setminus \{4\}$$. 2. **Recall the zero of a rational function:** A rational function $$\frac{f(x)}{g(x)}$$ is zero where the numerator $$f(x)$$ is zero and the denominator $$g(x)$$ is not zero. 3. **Set the numerator equal to zero:** $$x^2 - 16 = 0$$ 4. **Factor the numerator:** $$x^2 - 16 = (x - 4)(x + 4)$$ 5. **Solve for zeros:** $$ (x - 4)(x + 4) = 0 \implies x = 4 \text{ or } x = -4 $$ 6. **Check domain restrictions:** Since $$x = 4$$ is excluded from the domain, it cannot be a zero of $$g(x)$$. 7. **Final answer:** The only zero of $$g(x)$$ is $$x = -4$$.