1. **State the problem:** Simplify the expression $$\frac{x^2}{x-3} - \frac{9}{x-3}$$. 2. **Identify the common denominator:** Both terms have the same denominator $x-3$, so we can combine the numerators directly. 3. **Combine the fractions:** $$\frac{x^2}{x-3} - \frac{9}{x-3} = \frac{x^2 - 9}{x-3}$$ 4. **Factor the numerator:** Recognize that $x^2 - 9$ is a difference of squares: $$x^2 - 9 = (x - 3)(x + 3)$$ 5. **Simplify the fraction:** $$\frac{(x - 3)(x + 3)}{x - 3}$$ Since $x \neq 3$ (to avoid division by zero), we can cancel $x - 3$: $$= x + 3$$ 6. **Final answer:** The simplified expression is $$x + 3$$. **Therefore, the correct option is Option 3: $x + 3$.