Factorise :
` x^(2) - (8)/(x)`

Answer

To factorize the expression \( x^2 - \frac{8}{x} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ x^2 - \frac{8}{x} \]
To combine the terms, we can take a common denominator. The common denominator here is \( x \).

### Step 2: Take the LCM
We rewrite the expression with the common denominator:
\[ x^2 - \frac{8}{x} = \frac{x^3}{x} - \frac{8}{x} = \frac{x^3 - 8}{x} \]

### Step 3: Recognize the difference of cubes
Now we have:
\[ \frac{x^3 - 8}{x} \]
We can see that \( 8 \) is \( 2^3 \), so we can rewrite it as:
\[ x^3 - 2^3 \]
This is a difference of cubes, which can be factored using the formula:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
where \( a = x \) and \( b = 2 \).

### Step 4: Apply the difference of cubes formula
Using the formula, we factor \( x^3 - 2^3 \):
\[ x^3 - 2^3 = (x - 2)(x^2 + 2x + 4) \]

### Step 5: Write the final factorized form
Now, substituting back into our expression, we have:
\[ \frac{(x - 2)(x^2 + 2x + 4)}{x} \]

Thus, the factorized form of the original expression \( x^2 - \frac{8}{x} \) is:
\[ \frac{(x - 2)(x^2 + 2x + 4)}{x} \]

### Summary
The final answer is:
\[ \frac{(x - 2)(x^2 + 2x + 4)}{x} \]