Question

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

Answer 1

$$\begin{gathered} (\frac{65}{12}+\frac{12}{7})÷(\frac{65}{12}-\frac{12}{7}) \\ =\frac{65\times 7+12\times 12}{84}÷\frac{65\times 7-12\times 12}{84} \\ =\frac{455+144}{84}÷\frac{455-144}{84} \\ =\frac{599}{84}÷\frac{311}{84} \\ =\frac{599}{84}\times \frac{84}{311} \\ =\frac{599}{311} \end{gathered}$$