To simplify the expression \(\frac{6x^3 - 15x^2 - 3x}{3x}\), you can divide each term in the numerator by \(3x\).
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Split the terms in the numerator: \[ \frac{6x^3}{3x} - \frac{15x^2}{3x} - \frac{3x}{3x} \]
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Simplify each term:
- \(\frac{6x^3}{3x} = 2x^2\)
- \(\frac{15x^2}{3x} = 5x\)
- \(\frac{3x}{3x} = 1\)
Putting it all together: \[ 2x^2 - 5x - 1 \]
So, \(\frac{6x^3 - 15x^2 - 3x}{3x} = 2x^2 - 5x - 1\).