Divide the sum of `(65)/(12) and (8)/(3)` by their difference.

Answer

To solve the problem of dividing the sum of \( \frac{65}{12} \) and \( \frac{8}{3} \) by their difference, we can follow these steps:

### Step 1: Find the sum of \( \frac{65}{12} \) and \( \frac{8}{3} \).

To add these two fractions, we need a common denominator. The denominators are 12 and 3. The least common multiple (LCM) of 12 and 3 is 12.

Now, we convert \( \frac{8}{3} \) to have a denominator of 12:
\[ \frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12} \]

Now we can add the two fractions:
\[ \frac{65}{12} + \frac{32}{12} = \frac{65 + 32}{12} = \frac{97}{12} \]

### Step 2: Find the difference of \( \frac{65}{12} \) and \( \frac{8}{3} \).

Using the same common denominator of 12, we can subtract:
\[ \frac{65}{12} - \frac{32}{12} = \frac{65 - 32}{12} = \frac{33}{12} \]

### Step 3: Divide the sum by the difference.

Now we need to divide the sum \( \frac{97}{12} \) by the difference \( \frac{33}{12} \):
\[ \frac{97}{12} \div \frac{33}{12} \]

When dividing fractions, we multiply by the reciprocal:
\[ \frac{97}{12} \times \frac{12}{33} \]

The 12s in the numerator and denominator cancel out:
\[ \frac{97}{33} \]

### Final Answer:
The final result is:
\[ \frac{97}{33} \]

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