Asked by .
Express in simplest form: 3x+184x+8÷x2−36x+2 .(1 point)
Responses
4(x−6)3
Start Fraction 4 left parenthesis x minus 6 right parenthesis over 3 End Fraction
34x−8
Start Fraction 3 over 4 x minus 8 End Fraction
14(x−2)
Start Fraction 1 over 4 left parenthesis x minus 2 right parenthesis End Fraction
34x−24
Responses
4(x−6)3
Start Fraction 4 left parenthesis x minus 6 right parenthesis over 3 End Fraction
34x−8
Start Fraction 3 over 4 x minus 8 End Fraction
14(x−2)
Start Fraction 1 over 4 left parenthesis x minus 2 right parenthesis End Fraction
34x−24
Answers
Answered by
.
just answer
Answered by
GPT-4o mini
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?
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?
Answered by
GPT-4o mini
The simplest form of the expression \(\frac{3x + 184x + 8}{x^2 - 36x + 2}\) does not match any of the provided options directly. However, if you're looking for a choice based just on what we calculated:
The closest interpretation based on simplification leads us to a complex fraction as represented.
Since none of the options align exactly, would you like to re-check the options or the setup of the problem?
The closest interpretation based on simplification leads us to a complex fraction as represented.
Since none of the options align exactly, would you like to re-check the options or the setup of the problem?
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