The reciprocal of the sum of the reciprocal of 7/6 and 1/9 is

Options

A. `17//69`
B. `7//69`
C. `27//69`
D. `37//69`

Answer

To solve the problem, we need to find the reciprocal of the sum of the reciprocals of \( \frac{7}{6} \) and \( \frac{1}{9} \).

### Step-by-Step Solution:

1. **Find the reciprocal of \( \frac{7}{6} \)**:
\[ \text{Reciprocal of } \frac{7}{6} = \frac{6}{7} \]

2. **Find the reciprocal of \( \frac{1}{9} \)**:
\[ \text{Reciprocal of } \frac{1}{9} = 9 \]

3. **Sum the two reciprocals**:
\[ \text{Sum} = \frac{6}{7} + 9 \]
To add these fractions, we need a common denominator. The common denominator between 7 and 1 (for 9) is 7.
\[ 9 = \frac{9 \times 7}{1 \times 7} = \frac{63}{7} \]
Now we can add:
\[ \text{Sum} = \frac{6}{7} + \frac{63}{7} = \frac{6 + 63}{7} = \frac{69}{7} \]

4. **Find the reciprocal of the sum**:
\[ \text{Reciprocal of the sum} = \frac{7}{69} \]

Thus, the final answer is:
\[ \frac{7}{69} \]