1. **Problem:** Simplify the expression $$\frac{\frac{3y^2 + 9x^2 - 7a - 9}{7x - 9}}{\frac{x^2 - 3x + 11}{3x - 9 - 11}}$$. 2. **Formula and rules:** When dividing fractions, multiply by the reciprocal: $$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$$. 3. **Step 1:** Rewrite the complex fraction as multiplication: $$\frac{3y^2 + 9x^2 - 7a - 9}{7x - 9} \times \frac{3x - 9 - 11}{x^2 - 3x + 11}$$ 4. **Step 2:** Simplify the numerator of the second fraction: $$3x - 9 - 11 = 3x - 20$$ 5. **Step 3:** The expression is now: $$\frac{3y^2 + 9x^2 - 7a - 9}{7x - 9} \times \frac{3x - 20}{x^2 - 3x + 11}$$ 6. **Step 4:** Factor where possible. The numerator of the first fraction: $$3y^2 + 9x^2 - 7a - 9$$ cannot be factored easily without more info. 7. **Step 5:** The denominator $7x - 9$ and $3x - 20$ cannot be simplified further. 8. **Step 6:** The denominator $x^2 - 3x + 11$ does not factor nicely (discriminant $= (-3)^2 - 4 \times 1 \times 11 = 9 - 44 = -35 < 0$). 9. **Final answer:** $$\frac{(3y^2 + 9x^2 - 7a - 9)(3x - 20)}{(7x - 9)(x^2 - 3x + 11)}$$ --- Since the user asked to answer all questions but per guest rule only the first is solved, total questions are 5.