What is $$\frac{{\frac{7}{8} \times \frac{7}{8} + \frac{5}{6} \times \frac{5}{6} + \frac{7}{8} \times \frac{5}{3}}}{{\frac{7}{8} \times \frac{7}{8} - \frac{5}{6} \times \frac{5}{6}}}$$     equal to ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given expression,}} \cr & \,\,\,\,\,\,\,\,\,\,\frac{{{{\left( {\frac{7}{8} + \frac{5}{6}} \right)}^2}}}{{{{\left( {\frac{7}{8}} \right)}^2} - {{\left( {\frac{5}{6}} \right)}^2}}} \cr & = \frac{{{{\left( {\frac{7}{8} + \frac{5}{6}} \right)}^2}}}{{\left( {\frac{7}{8} + \frac{5}{6}} \right)\left( {\frac{7}{8} - \frac{5}{6}} \right)}} \cr & = \frac{{\left( {\frac{7}{8} + \frac{5}{6}} \right)}}{{\left( {\frac{7}{8} - \frac{5}{6}} \right)}} \cr & = \left( {\frac{{41}}{{24}} \times 24} \right) \cr & = 41 \cr} $$