`x+1=2/(x+1)`
In the equation above, which of the following is a possible value of x + 1 ?

Options

A. `1-sqrt2`
B. `sqrt2`
C. 2
D. 4

Explanation

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

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

### Step 2: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ (x + 1)(x + 1) = 2 \]
This simplifies to:
\[ (x + 1)^2 = 2 \]

### Step 3: Take the square root of both sides
Next, we take the square root of both sides:
\[ x + 1 = \pm \sqrt{2} \]

### Step 4: Solve for \( x + 1 \)
This gives us two possible values for \( x + 1 \):
\[ x + 1 = \sqrt{2} \quad \text{or} \quad x + 1 = -\sqrt{2} \]

### Step 5: Identify possible values
From the options given (1, -√2, √2, 2, 4), we see that one of the possible values of \( x + 1 \) is:
\[ \sqrt{2} \]

Thus, the answer is:
\[ \text{Possible value of } x + 1 \text{ is } \sqrt{2}. \]