Question

Simplify: ${\displaystyle \frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times \frac{3}{5}}}$

Answer 1

Given, ${\displaystyle \frac{\frac{1}{4}+\frac{1}{5}}{1-\frac{3}{8}\times \frac{3}{5}}}$

= ${\displaystyle \frac{\frac{5 + 4}{20}}{1-\frac{9}{40}}}$

= ${\displaystyle \frac{\frac{9}{20}}{\frac{40 - 9}{40}}}$

= ${\displaystyle \frac{\frac{9}{20}}{\frac{31}{40}}}$

= ${\displaystyle \frac{9}{20}\times \frac{40}{31}}$  ......${\displaystyle [\because \text{Reciprocal of} \frac{31}{40}=\frac{40}{31}]}$

= ${\displaystyle \frac{18}{31}}$