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 can follow these steps:

### Step 1: Cross Multiply
We start by cross-multiplying to eliminate the fractions:
\[ 1 \cdot (x - 2) = 2 \cdot (x - 1) \]
This simplifies to:
\[ x - 2 = 2(x - 1) \]

### Step 2: Distribute on the Right Side
Now, we distribute the 2 on the right side:
\[ x - 2 = 2x - 2 \]

### Step 3: Rearrange the Equation
Next, we will rearrange the equation to isolate the variable \(x\). We can move all terms involving \(x\) to one side and constant terms to the other side:
\[ x - 2x = -2 + 2 \]
This simplifies to:
\[ -x = 0 \]

### Step 4: Solve for \(x\)
Now, we can solve for \(x\) by multiplying both sides by -1:
\[ x = 0 \]

### Conclusion
Thus, the value of \(x\) that satisfies the equation is:
\[ \boxed{0} \]

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