Question

Divide the sum of $\frac{65}{12}$and $\frac{12}{7}$ by their difference.

Answer 1

The sum is$=\frac{65}{12}+\frac{12}{7}=\frac{65\times 7+12\times 12}{84}=\frac{455+144}{84}$

$\Rightarrow \frac{599}{84}$

The difference is $=\frac{65}{12}-\frac{12}{7}=\frac{65\times 7-12\times 12}{84}=\frac{455-144}{84}$

$\Rightarrow \frac{311}{84}$

on division of sum by difference of these two numbers$=\frac{{\displaystyle \raisebox{1ex}{$599$}\!\left/ \!\raisebox{-1ex}{$84$}\right.}}{{\displaystyle \raisebox{1ex}{$311$}\!\left/ \!\raisebox{-1ex}{$84$}\right.}}=\frac{599}{311}$

Hence, $\frac{599}{311}$ is the correct answer.