1. **State the problem:** Simplify the expression \(\frac{16x^2y - x^5 y^3}{x^2 y} - \frac{9d^6 e^5 - 15d^7 e^3 + 12 d^8 e^4}{3 d^3 e^2}\). 2. **Simplify the first fraction:** \[\frac{16x^2y - x^5 y^3}{x^2 y} = \frac{16x^2y}{x^2 y} - \frac{x^5 y^3}{x^2 y}\] 3. Cancel common factors in each term: \[\frac{16\cancel{x^2}\cancel{y}}{\cancel{x^2}\cancel{y}} - \frac{x^5 y^3}{x^2 y} = 16 - \frac{x^{5-2} y^{3-1}}{1} = 16 - x^3 y^2\] 4. **Simplify the second fraction:** \[\frac{9d^6 e^5 - 15d^7 e^3 + 12 d^8 e^4}{3 d^3 e^2} = \frac{9d^6 e^5}{3 d^3 e^2} - \frac{15d^7 e^3}{3 d^3 e^2} + \frac{12 d^8 e^4}{3 d^3 e^2}\] 5. Simplify each term by canceling common factors: \[\frac{9\cancel{d^6} e^5}{3 \cancel{d^3} e^2} = 3 d^{6-3} e^{5-2} = 3 d^3 e^3\] \[\frac{15 d^7 e^3}{3 d^3 e^2} = 5 d^{7-3} e^{3-2} = 5 d^4 e\] \[\frac{12 d^8 e^4}{3 d^3 e^2} = 4 d^{8-3} e^{4-2} = 4 d^5 e^2\] 6. Combine the simplified terms: \[3 d^3 e^3 - 5 d^4 e + 4 d^5 e^2\] 7. **Final simplified expression:** \[16 - x^3 y^2 - (3 d^3 e^3 - 5 d^4 e + 4 d^5 e^2) = 16 - x^3 y^2 - 3 d^3 e^3 + 5 d^4 e - 4 d^5 e^2\] This is the quotient simplified.