1. **State the problem:** Simplify the expression $$\frac{x^2 - 4x}{x^2 - 9}$$. 2. **Recall the formulas and rules:** - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Factor common terms when possible. 3. **Factor numerator and denominator:** - Numerator: $$x^2 - 4x = x(x - 4)$$ - Denominator: $$x^2 - 9 = (x - 3)(x + 3)$$ 4. **Rewrite the expression:** $$\frac{x(x - 4)}{(x - 3)(x + 3)}$$ 5. **Check for common factors:** - There are no common factors between numerator and denominator. 6. **State the simplified form:** The expression cannot be simplified further, so the simplified form is: $$\frac{x(x - 4)}{(x - 3)(x + 3)}$$ 7. **Domain restrictions:** - Denominator cannot be zero, so $$x \neq 3$$ and $$x \neq -3$$. **Final answer:** $$\frac{x(x - 4)}{(x - 3)(x + 3)}$$