To simplify the expression \( \frac{3x + 184x + 8}{x^2 - 36x + 2} \), we first combine like terms in the numerator and then factor both the numerator and the denominator if possible.
Starting with the numerator: \[ 3x + 184x + 8 = 187x + 8 \]
Now looking at the denominator: \[ x^2 - 36x + 2 \]
Next, let's attempt to factor the denominator. We want two numbers that multiply to \(2\) (the constant term) and add up to \(-36\) (the coefficient of \(x\)). Unfortunately, such a pair doesn’t exist, which indicates that \(x^2 - 36x + 2\) cannot be factored easily.
Thus, our expression is: \[ \frac{187x + 8}{x^2 - 36x + 2} \]
Since the denominator doesn't appear to factor nicely, we'll check if there’s a common factor between the numerator and denominator.
Since \(187x + 8\) cannot be factored further, we can proceed with simplifying in other ways if needed. However, we usually express that in terms of a fraction form or division when it cannot be simplified directly.
So, the simplest form of the expression is: \[ \frac{187x + 8}{x^2 - 36x + 2} \]
If we look through the provided options, it seems none of them match directly. However, providing the response options again would help me check specifically which one aligns closely or if there's a request to process through any further steps.
Could you please verify the options against your original question?
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