To simplify the expression \( 3x + 184x + \frac{8}{x^2 - 36x + 2} \), first, we should combine like terms and then look at the fraction.
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Combine the terms in the numerator: \[ 3x + 184x = 187x \] So the expression simplifies to: \[ 187x + \frac{8}{x^2 - 36x + 2} \]
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Next, look at the quadratic \( x^2 - 36x + 2 \). Unfortunately, it doesn't factor nicely, so we'll leave it as is for now.
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Now the full expression is: \[ 187x + \frac{8}{x^2 - 36x + 2} \]
Given the options and what we have, let's find a common way to express or simplify it further. The answer choices seem to indicate a fractional form, which typically involves common denominators or factorizations. Since the polynomial does not factor simply, we need to leave the quadratic form in our expression.
None of the following options directly match what we've derived:
- \( 34x - 24 \)
- \( \frac{2}{4x - 24} \)
- \( 34x - 8 \)
- \( \frac{3}{4(x - 2)} \)
- \( \frac{4(x - 6)}{3} \)
After reviewing the options and the expression derived, it appears the likely answer must be derived from the simplified form after cross-multiplying or approximating.
Thus, the expression in simplest terms most appropriate from the given options is not immediately clear, as they seem to involve more involved manipulations or approximations.
To identify which expressions might work, we might try things like setting the denominator to zero, checking values, or matching polynomial degrees, etc.
However, based on the analysis, simplify further might not yield simple expressions resembling those presented centered on factoring, rational expressions, or fundamental terms that leverage constants or simple arithmetic combined with \( x \) terms.
If we had to choose based on visual inspection or exclusivity, it would appear that none of the responses simplify from \( 187x + \frac{8}{x^2 - 36x + 2} \). Maybe clarifying the desired operations or the manipulation intended might yield the solid answer.
In conclusion, the options appear not to correspond to what would typically simplify from that expression you began with; was there a particular restricted parameter or additional algebraic method expected in your query? Or was checking with substitutive terms needed indicating possible errors in the generation?
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