if the equality `1/x-1 = 2/x-2` is satisfied by x then the value of x will be :

Options

A. 2
B. 1
C. `1/2`
D. 0

Answer

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

### Step 1: Rearrange the equation
Start by moving all terms involving \( x \) to one side and constant terms to the other side.

\[ \frac{1}{x} - \frac{2}{x} = -2 + 1 \]

### Step 2: Simplify the left side
Combine the fractions on the left side:

\[ \frac{1 - 2}{x} = -1 \]

This simplifies to:

\[ \frac{-1}{x} = -1 \]

### Step 3: Eliminate the negative signs
Multiply both sides by -1 to make the equation easier to work with:

\[ \frac{1}{x} = 1 \]

### Step 4: Solve for \( x \)
Now, take the reciprocal of both sides:

\[ x = 1 \]

Thus, the value of \( x \) that satisfies the equation is:

\[ \boxed{1} \]

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