To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can start by factoring the numerator.
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Factor the numerator \(4x^2 - 12x + 24\): \[ 4x^2 - 12x + 24 = 4(x^2 - 3x + 6) \]
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Now we can rewrite the expression: \[ \frac{4(x^2 - 3x + 6)}{4x} \]
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The \(4\) in the numerator and denominator cancel out: \[ \frac{x^2 - 3x + 6}{x} \]
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Now we can separate the terms in the numerator: \[ \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x} = x - 3 + \frac{6}{x} \]
Putting it all together, the simplified expression in standard form is: \[ x - 3 + \frac{6}{x} \]
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