Simplify : $$\frac{{1 + \frac{1}{2}}}{{1 - \frac{1}{2}}} \div \frac{4}{7}\left( {\frac{2}{5} + \frac{3}{{10}}} \right)$$     $${\text{of}}$$ $$\frac{{\frac{1}{2} + \frac{1}{3}}}{{\frac{1}{2} - \frac{1}{3}}}$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to question,}} \cr & \frac{{1 + \frac{1}{2}}}{{1 - \frac{1}{2}}} \div \frac{4}{7}\left( {\frac{2}{5} + \frac{3}{{10}}} \right){\text{of }}\frac{{\frac{1}{2} + \frac{1}{3}}}{{\frac{1}{2} - \frac{1}{3}}} \cr & = \frac{{\frac{3}{2}}}{{\frac{1}{2}}} \div \frac{4}{7}\left( {\frac{{20 + 15}}{{50}}} \right) \times \frac{{\frac{5}{6}}}{{\frac{1}{6}}} \cr & = \frac{3}{2} \times \frac{2}{1} \div \frac{4}{7} \times \frac{{35}}{{50}} \times \frac{5}{6} \times \frac{6}{1} \cr & = \frac{3}{2} \times \frac{2}{1} \div 2 \cr & = \frac{3}{2} \times 2 \div \frac{1}{2} \cr & = \frac{3}{2} \cr} $$