To simplify the expression \(\frac{18x^2 - 12x + 6}{3x}\), we can start by factoring out the common factor from the numerator.
First, we notice that each term in the numerator, \(18x^2\), \(-12x\), and \(6\) has a common factor of \(6\):
\[ 18x^2 - 12x + 6 = 6(3x^2 - 2x + 1) \]
Now, we can rewrite the entire expression:
\[ \frac{18x^2 - 12x + 6}{3x} = \frac{6(3x^2 - 2x + 1)}{3x} \]
Next, we simplify the fraction:
\[ = \frac{6}{3x}(3x^2 - 2x + 1) \]
The \(6\) and \(3\) simplify:
\[ = \frac{6}{3} \cdot \frac{(3x^2 - 2x + 1)}{x} = 2 \cdot \frac{(3x^2 - 2x + 1)}{x} = 2(3x - 2 + \frac{1}{x}) = 6x - 4 + \frac{2}{x} \]
Now we can organize our simplified terms:
This leads us to:
\[ 6x - 4 + \frac{2}{x} \]
So the simplified form of the expression is:
Option D: \(6x - 4 + \frac{2}{x}\).