To find an equivalent form of the rational expression \(-3x^2 - 15x - 18x + 3\), we first need to simplify it.
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Combine like terms in the expression: \[ -3x^2 - 15x - 18x + 3 = -3x^2 - 33x + 3 \]
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Next, we can factor the expression. We first factor out \(-3\): \[ -3(x^2 + 11x - 1) \] We should check if we can factor \(x^2 + 11x - 1\) further, but in this case it's not easily factored into rational numbers.
Since the original problem doesn't present any denominators or other forms, it's hard to say which of the given options (if any) are equivalent forms without additional context, especially since they seem to have different structures that may relate to factoring or rewriting.
Now let's analyze each response:
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This rational expression does not have any equivalent forms.
- This is incorrect; every rational expression has equivalent forms unless it is undefined.
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\(-3x - 24 - \frac{114}{x + 3}\)
- This does not seem to be an equivalent form based on our simplification of \(-3x^2 - 33x + 3\).
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\(-3x - 114\)
- This is not equivalent since it does not account for the original quadratic and is too simplified.
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\(-3x - 6\)
- This is also incorrect for the same reason as above.
Given the options presented, none of them correctly represent an equivalent form of the original rational expression after simplification. The expression itself maintains an inherent complexity that isn't captured in any of the responses provided.
In conclusion, the best answer based on given options is: This rational expression does not have any equivalent forms. - Although this response may not technically be true from the standpoint of rational expressions in general, based on the accuracy of the other options, it appears to be the most appropriate in this context.