1. **Simplify the expression:** $$\frac{1}{x} - \frac{3}{x^2} \cdot 1 - \frac{9}{x^2} \div \left(\frac{1}{x} + \frac{2}{x^2} \cdot 1 - \frac{4}{x^2}\right)$$ 2. **Rewrite the expression carefully:** $$\frac{\frac{1}{x} - \frac{3}{x^2} - \frac{9}{x^2}}{\frac{1}{x} + \frac{2}{x^2} - \frac{4}{x^2}}$$ 3. **Combine like terms in numerator and denominator:** Numerator: $$\frac{1}{x} - \frac{3}{x^2} - \frac{9}{x^2} = \frac{1}{x} - \frac{12}{x^2}$$ Denominator: $$\frac{1}{x} + \frac{2}{x^2} - \frac{4}{x^2} = \frac{1}{x} - \frac{2}{x^2}$$ 4. **Find common denominator $x^2$ for numerator and denominator:** Numerator: $$\frac{x}{x^2} - \frac{12}{x^2} = \frac{x - 12}{x^2}$$ Denominator: $$\frac{x}{x^2} - \frac{2}{x^2} = \frac{x - 2}{x^2}$$ 5. **Divide numerator by denominator:** $$\frac{\frac{x - 12}{x^2}}{\frac{x - 2}{x^2}} = \frac{x - 12}{x^2} \times \frac{x^2}{x - 2} = \frac{x - 12}{x - 2}$$ 6. **Final simplified expression:** $$\boxed{\frac{x - 12}{x - 2}}$$ --- This is the solution to the first problem only as per instructions.