Question:
Divide the sum of $\frac{65}{12}$ and $\frac{12}{7}$ by their difference.
Solution:
$\left(\frac{65}{12}+\frac{12}{7}\right) \div\left(\frac{65}{12}-\frac{12}{7}\right)$
$=\frac{65 \times 7+12 \times 12}{84} \div \frac{65 \times 7-12 \times 12}{84}$
$=\frac{455+144}{84} \div \frac{455-144}{84}$
$=\frac{599}{84} \div \frac{311}{84}$
$=\frac{599}{84} \times \frac{84}{311}$
$=\frac{599}{311}$
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