1. The problem asks to express the division of two fractions as a single simplified fraction: $$\frac{9pq}{2+q} \div \frac{3pq-6q}{4-q^2}$$ 2. Recall the rule for dividing fractions: dividing by a fraction is the same as multiplying by its reciprocal. 3. Rewrite the expression using multiplication by the reciprocal: $$\frac{9pq}{2+q} \times \frac{4-q^2}{3pq-6q}$$ 4. Factor where possible: - Factor the numerator and denominator of the second fraction: $$4 - q^2 = (2 - q)(2 + q)$$ $$3pq - 6q = 3q(p - 2)$$ 5. Substitute the factored forms: $$\frac{9pq}{2+q} \times \frac{(2 - q)(2 + q)}{3q(p - 2)}$$ 6. Multiply the numerators and denominators: $$\frac{9pq \times (2 - q)(2 + q)}{(2 + q) \times 3q(p - 2)}$$ 7. Cancel common factors: - Cancel $(2 + q)$ from numerator and denominator: $$\frac{9pq \times \cancel{(2 + q)} (2 - q)}{\cancel{(2 + q)} \times 3q(p - 2)}$$ - Cancel $3q$ from numerator and denominator: $$\frac{\cancel{3} \times 3 p \cancel{q} (2 - q)}{\cancel{3} \times \cancel{q} (p - 2)} = \frac{3p(2 - q)}{p - 2}$$ 8. The simplified single fraction is: $$\boxed{\frac{3p(2 - q)}{p - 2}}$$ This matches option D.