`(3^(0)+3^(-1))/(3^(-1)-3^(0))` is simplified to

Options

A. `-2`
B. `-1`
C. `1`
D. `2`

Answer

To simplify the expression \((3^{0} + 3^{-1}) / (3^{-1} - 3^{0})\), we can follow these steps:

### Step 1: Simplify \(3^{0}\) and \(3^{-1}\)
We know that:
- \(3^{0} = 1\)
- \(3^{-1} = \frac{1}{3}\)

So we can rewrite the expression as:
\[ \frac{(1 + \frac{1}{3})}{(\frac{1}{3} - 1)} \]

### Step 2: Simplify the numerator
Now, let's simplify the numerator:
\[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \]

### Step 3: Simplify the denominator
Next, we simplify the denominator:
\[ \frac{1}{3} - 1 = \frac{1}{3} - \frac{3}{3} = \frac{1 - 3}{3} = \frac{-2}{3} \]

### Step 4: Substitute back into the expression
Now we substitute the simplified numerator and denominator back into the expression:
\[ \frac{\frac{4}{3}}{\frac{-2}{3}} \]

### Step 5: Simplify the fraction
To simplify this fraction, we multiply by the reciprocal of the denominator:
\[ \frac{4}{3} \times \frac{3}{-2} = \frac{4 \cdot 3}{3 \cdot -2} = \frac{4}{-2} = -2 \]

### Final Answer
Thus, the simplified form of the expression \((3^{0} + 3^{-1}) / (3^{-1} - 3^{0})\) is:
\[ \boxed{-2} \]