Question

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

Answer 1

\[(\frac{65}{12} + \frac{12}{7}) \div (\frac{65}{12} - \frac{12}{7})\]
\[ = \frac{65 \times 7 + 12 \times 12}{84} \div \frac{65 \times 7 - 12 \times 12}{84}\]
\[ = \frac{455 + 144}{84} \div \frac{455 - 144}{84}\]
\[ = \frac{599}{84} \div \frac{311}{84}\]
\[ = \frac{599}{84} \times \frac{84}{311}\]
\[ = \frac{599}{311}\]