1. **State the problem:** Simplify the expression $$\frac{-3x^4 - 3x^3 - 9x^2}{3x^2}$$. 2. **Formula and rules:** When simplifying a fraction with polynomials, divide each term in the numerator by the denominator separately. 3. **Divide each term:** $$\frac{-3x^4}{3x^2} + \frac{-3x^3}{3x^2} + \frac{-9x^2}{3x^2}$$ 4. **Simplify each term:** - For $$\frac{-3x^4}{3x^2}$$, cancel common factors: $$\frac{\cancel{-3}x^{4}}{\cancel{3}x^{2}} = -x^{4-2} = -x^{2}$$ - For $$\frac{-3x^3}{3x^2}$$, cancel common factors: $$\frac{\cancel{-3}x^{3}}{\cancel{3}x^{2}} = -x^{3-2} = -x$$ - For $$\frac{-9x^2}{3x^2}$$, cancel common factors: $$\frac{\cancel{-9}x^{2}}{\cancel{3}x^{2}} = -3$$ 5. **Combine simplified terms:** $$-x^{2} - x - 3$$ 6. **Final answer:** $$\boxed{-x^{2} - x - 3}$$