To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can start by factoring the numerator.
The numerator \(4x^2 - 12x + 24\) can be factored out by taking out the common factor of 4:
\[ 4(x^2 - 3x + 6) \]
Now substituting this back into the fraction gives:
\[ \frac{4(x^2 - 3x + 6)}{4x} \]
Next, we can cancel the \(4\) in the numerator and denominator:
\[ \frac{x^2 - 3x + 6}{x} \]
Now, we can separate this into two terms:
\[ \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x} \]
This simplifies to:
\[ x - 3 + \frac{6}{x} \]
Thus, the simplified form of the expression is:
\[ x - 3 + \frac{6}{x} \]
This can be left in this form, so the final answer in standard form is:
\[ x - 3 + \frac{6}{x} \]
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