If `abc=6 and a+b+c=6`, then find the value of `(1)/(ac)+(1)/(ab)+(1)/(bc)`.

Options

A. 2
B. 1
C. 3
D. 0

Answer

To solve the problem, we need to find the value of \(\frac{1}{ac} + \frac{1}{ab} + \frac{1}{bc}\) given that \(abc = 6\) and \(a + b + c = 6\).

### Step-by-step Solution:

1. **Write the expression**:
We start with the expression we need to evaluate:
\[ \frac{1}{ac} + \frac{1}{ab} + \frac{1}{bc} \]

2. **Find a common denominator**:
The common denominator for the three fractions is \(abc\). Therefore, we can rewrite the expression as:
\[ \frac{b}{abc} + \frac{c}{abc} + \frac{a}{abc} \]

3. **Combine the fractions**:
Now, we can combine the fractions:
\[ \frac{b + c + a}{abc} \]

4. **Substitute the known values**:
We know from the problem that \(a + b + c = 6\) and \(abc = 6\). Substituting these values into the expression gives us:
\[ \frac{6}{6} \]

5. **Simplify the expression**:
Simplifying \(\frac{6}{6}\) results in:
\[ 1 \]

Thus, the value of \(\frac{1}{ac} + \frac{1}{ab} + \frac{1}{bc}\) is \(1\).

### Final Answer:
The final answer is \(1\).