Simplify the following equation:
​$$\left( 4 \frac{3}{4} - 3 \frac{1}{3} \right) \div \left( \frac{3}{4} - \frac{3}{5} \right) + \frac{3}{5} \times \frac{5}{7} \times \frac{7}{9}$$​​

Correct option is A

Given:

​$$\left( 4 \frac{3}{4} - 3 \frac{1}{3} \right) \div \left( \frac{3}{4} - \frac{3}{5} \right) + \frac{3}{5} \times \frac{5}{7} \times \frac{7}{9}$$​​

Solution:

​$$\left( 4 \frac{3}{4} - 3 \frac{1}{3} \right) \div \left( \frac{3}{4} - \frac{3}{5} \right) + \frac{3}{5} \times \frac{5}{7} \times \frac{7}{9}$$​​

=$$\left( \frac{19}{4} - \frac{10}{3} \right) \div \left( \frac{3}{4} - \frac{3}{5} \right) + \frac{3}{5} \times \frac{5}{7} \times \frac{7}{9}$$ 

=$$\frac{19}{4} - \frac{10}{3} = \frac{17}{12}, \quad \frac{3}{4} - \frac{3}{5} = \frac{3}{20}$$ 

=$$\left( \frac{17}{12} \right) \div \left( \frac{3}{20} \right) + \frac{3}{5} \times \frac{5}{7} \times \frac{7}{9}$$ 

=$$\frac{85}{9} + \frac{1}{3} = \frac{85}{9} + \frac{3}{9} = \frac{88}{9}$$ 

=$$9\frac{7}{9}$$​​