1. **State the problem:** Simplify the expression $$\frac{x^2 - 4x}{x^2 - 9}$$. 2. **Recall the formulas and rules:** - Factor quadratic expressions when possible. - Remember the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$. - Simplify by canceling common factors in numerator and denominator. 3. **Factor the numerator:** $$x^2 - 4x = x(x - 4)$$. 4. **Factor the denominator:** $$x^2 - 9 = (x - 3)(x + 3)$$ (difference of squares). 5. **Rewrite the expression with factors:** $$\frac{x(x - 4)}{(x - 3)(x + 3)}$$. 6. **Check for common factors:** There are no common factors between numerator and denominator. 7. **Final simplified form:** $$\frac{x(x - 4)}{(x - 3)(x + 3)}$$. **Note:** The expression is undefined at $$x = 3$$ and $$x = -3$$ because the denominator is zero there.