Question

subtract. write the answer as a fraction in lowest terms or as an integer.

\\(\frac{x}{9y} - \frac{7x}{9y}\\)

• \\(\frac{2}{3y}\\)
• \\(\frac{2x}{3y}\\)
• \\(-\frac{2}{3y}\\)
• \\(-\frac{2x}{3y}\\)

Explanation:

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],
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</pre_analysis>

<reasoning>

Subtract the numerators over the common denominator

\[
\frac{x}{9y} - \frac{7x}{9y} = \frac{x - 7x}{9y} = \frac{-6x}{9y}
\]

Simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor

\[
\frac{-6x}{9y} = \frac{-2x \cdot 3}{3y \cdot 3} = -\frac{2x}{3y}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{2}{3y}\)</mcq-option>
<mcq-option>(B) \(\frac{2x}{3y}\)</mcq-option>
<mcq-option>(C) \(-\frac{2}{3y}\)</mcq-option>
<mcq-correct>(D) \(-\frac{2x}{3y}\)</mcq-correct>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Subtracting Rational Expressions"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
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</pre_analysis>

<reasoning>

Subtract the numerators over the common denominator

\[
\frac{x}{9y} - \frac{7x}{9y} = \frac{x - 7x}{9y} = \frac{-6x}{9y}
\]

Simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor

\[
\frac{-6x}{9y} = \frac{-2x \cdot 3}{3y \cdot 3} = -\frac{2x}{3y}
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{2}{3y}\)</mcq-option>
<mcq-option>(B) \(\frac{2x}{3y}\)</mcq-option>
<mcq-option>(C) \(-\frac{2}{3y}\)</mcq-option>
<mcq-correct>(D) \(-\frac{2x}{3y}\)</mcq-correct>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
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