If `(4)/(x-1)=(x+1)/(2)`, which of the following is apossible value of x?

Options

A. `-1`
B. `1`
C. `2`
D. `3`

Answer

To solve the equation \(\frac{4}{x-1} = \frac{x+1}{2}\), we will follow these steps:

### Step 1: Cross Multiply
We start by cross-multiplying to eliminate the fractions:
\[ 4 \cdot 2 = (x + 1)(x - 1) \]
This simplifies to:
\[ 8 = (x + 1)(x - 1) \]

### Step 2: Use the Difference of Squares Formula
The right-hand side can be recognized as a difference of squares:
\[ (x + 1)(x - 1) = x^2 - 1 \]
Thus, we can rewrite the equation as:
\[ 8 = x^2 - 1 \]

### Step 3: Rearrange the Equation
Next, we rearrange the equation to isolate \(x^2\):
\[ x^2 = 8 + 1 \]
This simplifies to:
\[ x^2 = 9 \]

### Step 4: Take the Square Root
Now, we take the square root of both sides:
\[ x = \pm 3 \]

### Step 5: Identify Possible Values
The possible values of \(x\) are:
\[ x = 3 \quad \text{or} \quad x = -3 \]

### Step 6: Check the Options
Since the question asks for a possible value of \(x\) and we need to identify which of these values is given in the options, we find that \(3\) is a possible value.

### Final Answer
Thus, the possible value of \(x\) is:
\[ \boxed{3} \]