Question

question

evaluate \\(\frac{x^2 + 1}{x^2 - 3x + 2}\\) for the value \\(x = 3\\).

provide your answer below:

Explanation:

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"concepts_used": [
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</pre_analysis>

<reasoning>

Substitute the value into the numerator

Using the Evaluating Functions knowledge point
\[
3^2 + 1 = 9 + 1 = 10
\]

Substitute the value into the denominator

Using the Evaluating Functions knowledge point
\[
3^2 - 3(3) + 2 = 9 - 9 + 2 = 2
\]

Simplify the resulting fraction

Using the Fraction Arithmetic knowledge point
\[
\frac{10}{2} = 5
\]
</reasoning>

<answer>
Evaluate \(\frac{x^2 + 1}{x^2 - 3x + 2}\) for the value \(x = 3\).

Provide your answer below:
<blank>5</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Evaluating Rational Expressions"
]
}
</post_analysis>

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
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],
"needs_drawing": false,
"concepts_used": [
"Evaluating Functions",
"Fraction Arithmetic"
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"new_concepts": [
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"Fraction Arithmetic",
"Evaluating Rational Expressions"
]
}
</pre_analysis>

<reasoning>

Substitute the value into the numerator

Using the Evaluating Functions knowledge point
\[
3^2 + 1 = 9 + 1 = 10
\]

Substitute the value into the denominator

Using the Evaluating Functions knowledge point
\[
3^2 - 3(3) + 2 = 9 - 9 + 2 = 2
\]

Simplify the resulting fraction

Using the Fraction Arithmetic knowledge point
\[
\frac{10}{2} = 5
\]
</reasoning>

<answer>
Evaluate \(\frac{x^2 + 1}{x^2 - 3x + 2}\) for the value \(x = 3\).

Provide your answer below:
<blank>5</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Evaluating Rational Expressions"
]
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</post_analysis>