1. **State the problem:** Simplify the expression $$\frac{6ab - 3a^3}{21a^2 - 9ab^2}$$. 2. **Rewrite the expression:** The numerator is $6ab - 3a^3$ and the denominator is $21a^2 - 9ab^2$. 3. **Factor the numerator:** $$6ab - 3a^3 = 3a(2b - a^2)$$ 4. **Factor the denominator:** $$21a^2 - 9ab^2 = 3a(7a - 3b^2)$$ 5. **Rewrite the fraction with factored terms:** $$\frac{3a(2b - a^2)}{3a(7a - 3b^2)}$$ 6. **Cancel common factors:** Both numerator and denominator have $3a$, so cancel them: $$\frac{2b - a^2}{7a - 3b^2}$$ 7. **Final simplified form:** $$\boxed{\frac{2b - a^2}{7a - 3b^2}}$$ This is the simplest form since numerator and denominator share no further common factors.