1. **State the problem:** Simplify the expression \n $$\frac{\frac{2}{3}x^2 - 5x + \frac{7}{3}}{\frac{1}{3}x^2}$$\n and find which of the given options is equivalent.\n 2. **Recall the rule:** Dividing by a fraction is the same as multiplying by its reciprocal. Also, when dividing polynomials, divide each term in the numerator by the denominator.\n 3. **Rewrite the expression:**\n $$\frac{\frac{2}{3}x^2 - 5x + \frac{7}{3}}{\frac{1}{3}x^2} = \left(\frac{2}{3}x^2 - 5x + \frac{7}{3}\right) \div \left(\frac{1}{3}x^2\right)$$\n 4. **Divide each term separately:**\n $$= \frac{\frac{2}{3}x^2}{\frac{1}{3}x^2} - \frac{5x}{\frac{1}{3}x^2} + \frac{\frac{7}{3}}{\frac{1}{3}x^2}$$\n 5. **Simplify each term:**\n - First term: $$\frac{\frac{2}{3}x^2}{\frac{1}{3}x^2} = \frac{2}{3} \times \frac{3}{1} \times \frac{x^2}{x^2} = 2$$\n - Second term: $$\frac{5x}{\frac{1}{3}x^2} = 5x \times \frac{3}{1} \times \frac{1}{x^2} = 15 \times \frac{1}{x} = \frac{15}{x}$$\n - Third term: $$\frac{\frac{7}{3}}{\frac{1}{3}x^2} = \frac{7}{3} \times \frac{3}{1} \times \frac{1}{x^2} = 7 \times \frac{1}{x^2} = \frac{7}{x^2}$$\n 6. **Combine the terms with correct signs:**\n $$2 - \frac{15}{x} + \frac{7}{x^2}$$\n 7. **Compare with options:** This matches option A.\n **Final answer:** A\n