If `1-1/x=2-2/x`, then `3-3/x=`

Options

A. -3
B. `-1/3`
C. 0
D. `1/3`

Explanation

To solve the equation \(1 - \frac{1}{x} = 2 - \frac{2}{x}\), we will follow these steps:

### Step 1: Rearrange the equation
We start with the equation:
\[ 1 - \frac{1}{x} = 2 - \frac{2}{x} \]
We can rearrange this equation by moving all terms involving \(x\) to one side and constant terms to the other side.

### Step 2: Move terms
Rearranging gives us:
\[ 1 - 2 = -\frac{2}{x} + \frac{1}{x} \]
This simplifies to:
\[ -1 = -\frac{2}{x} + \frac{1}{x} \]

### Step 3: Combine like terms
Now, we can combine the fractions on the right side:
\[ -1 = -\frac{2 - 1}{x} \]
This simplifies to:
\[ -1 = -\frac{1}{x} \]

### Step 4: Remove the negative sign
Multiplying both sides by -1 gives:
\[ 1 = \frac{1}{x} \]

### Step 5: Solve for \(x\)
To find \(x\), we can take the reciprocal of both sides:
\[ x = 1 \]

### Step 6: Substitute \(x\) into \(3 - \frac{3}{x}\)
Now that we have \(x = 1\), we substitute this value into the expression \(3 - \frac{3}{x}\):
\[ 3 - \frac{3}{1} = 3 - 3 = 0 \]

### Conclusion
Thus, the value of \(3 - \frac{3}{x}\) is:
\[ \boxed{0} \]