1. **State the problem:** Simplify the expression $$\frac{x^2-5x-14}{x^2-9x+14}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and denominator and then cancel common factors. 3. **Factor the numerator:** $$x^2 - 5x - 14 = (x - 7)(x + 2)$$ 4. **Factor the denominator:** $$x^2 - 9x + 14 = (x - 7)(x - 2)$$ 5. **Rewrite the expression with factors:** $$\frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}$$ 6. **Cancel the common factor $(x - 7)$ (assuming $x \neq 7$ to avoid division by zero):** $$\frac{x + 2}{x - 2}$$ 7. **Final simplified form:** $$\frac{x + 2}{x - 2}$$ **Note:** The domain excludes $x = 7$ and $x = 2$ because they make the original denominator zero.