To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can first factor the numerator.
The numerator \(4x^2 - 12x + 24\) can be factored out by noticing that each term is divisible by 4:
\[ 4(x^2 - 3x + 6) \]
So we rewrite the expression as:
\[ \frac{4(x^2 - 3x + 6)}{4x} \]
Now, we can cancel the 4 in the numerator and the denominator:
\[ \frac{x^2 - 3x + 6}{x} \]
Next, we can separate the fraction:
\[ \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x} \]
This simplifies to:
\[ x - 3 + \frac{6}{x} \]
Thus, the simplified form of the expression in standard form is:
\[ x - 3 + \frac{6}{x} \]
If desired, we can also write it as:
\[ x - 3 + 6x^{-1} \]
However, the most straightforward standard form is:
\[ x - 3 + \frac{6}{x} \]
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