Explanation:

To solve the expression, follow these steps:

- Simplify the numerator:

- Convert mixed numbers to improper fractions:

- \(1\frac{4}{5} = \frac{9}{5}\) and \(3\frac{6}{7} = \frac{27}{7}\).

- Multiply \(\frac{3}{7} \times \frac{9}{5} = \frac{27}{35}\).

- Divide by \(\frac{27}{7}\): \(\frac{27}{35} \div \frac{27}{7} = \frac{27}{35} \times \frac{7}{27} = \frac{1}{5}\).

- \(\frac{5}{2} - \frac{1}{5} = \frac{23}{10}\).

- Simplify the denominator:

- Convert to improper fractions:

- \(1\frac{2}{5} = \frac{7}{5}\) and \(3\frac{1}{2} = \frac{7}{2}\) and \(1\frac{1}{4} = \frac{5}{4}\).

- Divide by \(\frac{7}{2}\): \(\frac{7}{5} \div \frac{7}{2} = \frac{2}{5}\).

- Multiply by \(\frac{5}{4}\): \(\frac{2}{5} \times \frac{5}{4} = \frac{1}{2}\).

- \( \frac{3}{2} + \frac{1}{2} = 2 \).

- Finalize:

- \(\frac{\frac{23}{10}}{2} = \frac{23}{20} = 1\frac{3}{20}\).

Option 3: \(1\frac{3}{20}\)