1. **State the problem:** Simplify the expression $$21 - \frac{7}{3x} \div \frac{7}{21x - 3}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal. 3. **Rewrite the expression:** $$21 - \frac{7}{3x} \times \frac{21x - 3}{7}$$ 4. **Simplify the multiplication:** $$21 - \frac{7}{3x} \times \frac{21x - 3}{7} = 21 - \frac{\cancel{7}}{3x} \times \frac{21x - 3}{\cancel{7}} = 21 - \frac{21x - 3}{3x}$$ 5. **Rewrite 21 as a fraction with denominator $3x$ to combine:** $$21 = \frac{21 \times 3x}{3x} = \frac{63x}{3x}$$ 6. **Subtract the fractions:** $$\frac{63x}{3x} - \frac{21x - 3}{3x} = \frac{63x - (21x - 3)}{3x} = \frac{63x - 21x + 3}{3x} = \frac{42x + 3}{3x}$$ 7. **Factor numerator:** $$\frac{42x + 3}{3x} = \frac{3(14x + 1)}{3x}$$ 8. **Cancel common factor 3:** $$\frac{\cancel{3}(14x + 1)}{\cancel{3}x} = \frac{14x + 1}{x}$$ **Final answer:** $$\frac{14x + 1}{x}$$