1. **Stating the problem:** Simplify the expression $$\frac{x^2 - 2x - 8}{x - 1}$$. 2. **Formula and rules:** To simplify a rational expression, factor the numerator and denominator if possible, then cancel common factors. 3. **Factor the numerator:** $$x^2 - 2x - 8 = (x - 4)(x + 2)$$ 4. **Rewrite the expression:** $$\frac{(x - 4)(x + 2)}{x - 1}$$ 5. **Check for common factors:** The denominator is $x - 1$, which does not match any factor in the numerator. 6. **Final simplified form:** Since no factors cancel, $$\frac{x^2 - 2x - 8}{x - 1} = \frac{(x - 4)(x + 2)}{x - 1}$$ 7. **Domain restriction:** $x \neq 1$ because the denominator cannot be zero. **Answer:** $$\frac{(x - 4)(x + 2)}{x - 1}$$