To simplify the expression
\[ \frac{-3x^4 - 3x^3 - 9x^2}{3x^2} \]
we can start by factoring out the common terms in the numerator.
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Factor out -3 from the numerator:
\[ -3(x^4 + x^3 + 3x^2) \]
Now the expression becomes:
\[ \frac{-3(x^4 + x^3 + 3x^2)}{3x^2} \]
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Cancel the common term (-3):
\[ \frac{-3}{3} \cdot \frac{x^4 + x^3 + 3x^2}{x^2} = -1 \cdot \frac{x^4 + x^3 + 3x^2}{x^2} \]
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Divide each term in the numerator by \(x^2\):
\[
- (x^4/x^2 + x^3/x^2 + 3x^2/x^2) = - (x^2 + x + 3) \]
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Final simplified expression:
\[
- (x^2 + x + 3) = -x^2 - x - 3 \]
Thus, the simplified form of the original expression is:
\[ -x^2 - x - 3 \]