In the equation `x -2 = (3)/(x -2),` which of the following is a possible value of `x -2` ?

Options

A. `sqrt3`
B. 1
C. `2 + sqrt3`
D. 3

Explanation

To solve the equation \( x - 2 = \frac{3}{x - 2} \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ x - 2 = \frac{3}{x - 2} \]

### Step 2: Multiply both sides by \( x - 2 \)
To eliminate the fraction, we multiply both sides by \( x - 2 \):
\[ (x - 2)(x - 2) = 3 \]

### Step 3: Simplify the left side
This simplifies to:
\[ (x - 2)^2 = 3 \]

### Step 4: Take the square root of both sides
Next, we take the square root of both sides:
\[ x - 2 = \pm \sqrt{3} \]

### Step 5: Solve for \( x - 2 \)
This gives us two possible values:
\[ x - 2 = \sqrt{3} \quad \text{or} \quad x - 2 = -\sqrt{3} \]

### Conclusion
The possible values of \( x - 2 \) are \( \sqrt{3} \) and \( -\sqrt{3} \). If we are looking for a possible value, we can choose \( \sqrt{3} \).