Simplify : $$\frac{{ - \frac{1}{2} - \frac{2}{3} + \frac{4}{5} - \frac{1}{3} + \frac{1}{5} + \frac{3}{4}}}{{\frac{1}{2} + \frac{2}{3} - \frac{4}{3} + \frac{1}{3} - \frac{1}{5} - \frac{4}{5}}}$$

Solution(By Examveda Team)

$$\eqalign{ & {\text{Given expression,}} \cr & \frac{{\left( { - \frac{2}{3} - \frac{1}{2}} \right) + \left( {\frac{4}{5} + \frac{1}{5}} \right) + \left( {\frac{3}{4} - \frac{1}{2}} \right)}}{{\left( {\frac{2}{3} - \frac{4}{3} + \frac{1}{3}} \right) - \left( {\frac{1}{5} + \frac{4}{5}} \right) + \frac{1}{2}}} \cr & = \frac{{ - 1 + 1 + \frac{1}{4}}}{{ - \frac{1}{3} - 1 + \frac{1}{2}}} \cr & = \frac{{\frac{1}{4}}}{{\frac{{ - 2 - 6 + 3}}{6}}} \cr & = \frac{{\frac{1}{4}}}{{ - \frac{5}{6}}} \cr & = \frac{1}{4} \times \left( { - \frac{6}{5}} \right) \cr & = - \frac{3}{{10}} \cr} $$