If ` x- (1)/ (x ) = 4`, find the value of :
` x+ (1)/(x)`

Answer

To solve the equation \( x - \frac{1}{x} = 4 \) and find the value of \( x + \frac{1}{x} \), we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ x - \frac{1}{x} = 4 \]

### Step 2: Square both sides
To eliminate the fraction, we square both sides:
\[ \left( x - \frac{1}{x} \right)^2 = 4^2 \]
This simplifies to:
\[ x^2 - 2 \cdot x \cdot \frac{1}{x} + \left( \frac{1}{x} \right)^2 = 16 \]
Which further simplifies to:
\[ x^2 - 2 + \frac{1}{x^2} = 16 \]

### Step 3: Rearrange the equation
Now, we can rearrange the equation:
\[ x^2 + \frac{1}{x^2} - 2 = 16 \]
Adding 2 to both sides gives:
\[ x^2 + \frac{1}{x^2} = 16 + 2 \]
Thus:
\[ x^2 + \frac{1}{x^2} = 18 \]

### Step 4: Use the identity for \( x + \frac{1}{x} \)
We know that:
\[ \left( x + \frac{1}{x} \right)^2 = x^2 + 2 + \frac{1}{x^2} \]
From our previous result, we can express it as:
\[ \left( x + \frac{1}{x} \right)^2 = 18 + 2 \]
This simplifies to:
\[ \left( x + \frac{1}{x} \right)^2 = 20 \]

### Step 5: Take the square root
Taking the square root of both sides gives:
\[ x + \frac{1}{x} = \sqrt{20} \quad \text{or} \quad x + \frac{1}{x} = -\sqrt{20} \]
Since \( x \) is a real number, we consider the positive root:
\[ x + \frac{1}{x} = 2\sqrt{5} \]

### Final Answer
Thus, the value of \( x + \frac{1}{x} \) is:
\[ \boxed{2\sqrt{5}} \]