what is the quotient?

\\frac{3y+2}{3y} \div \frac{6y^2+4y}{3y+2}\

* $\frac{1}{2y}$
* $\frac{3y+2}{6y^2}$
* $\frac{1}{y}$
* $\frac{2(3y+2)}{3}$

Question

what is the quotient?

\\frac{3y+2}{3y} \div \frac{6y^2+4y}{3y+2}\

* $\frac{1}{2y}$
* $\frac{3y+2}{6y^2}$
* $\frac{1}{y}$
* $\frac{2(3y+2)}{3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor" ], "new_concepts": [ "Rational Expression Division", "Simplifying Rational Expressions" ], "current_concepts": [ "Greatest Common Factor", "Rational Expression Division", "Simplifying Rational Expressions" ] } ## Rewrite division as multiplication Using the *Greatest Common Factor* knowledge point $$ \frac{3y+2}{3y} \div \frac{6y^2+4y}{3y+2} = \frac{3y+2}{3y} \cdot \frac{3y+2}{6y^2+4y} $$ ## Factor the denominator Using the *Greatest Common Factor* knowledge point $$ 6y^2 + 4y = 2y(3y + 2) $$ ## Substitute and simplify Using the *Greatest Common Factor* knowledge point $$ \frac{3y+2}{3y} \cdot \frac{3y+2}{2y(3y+2)} = \frac{3y+2}{3y \cdot 2y} = \frac{3y+2}{6y^2} $$

(A) $\frac{1}{2y}$

(B) $\frac{3y+2}{6y^2}$

(C) $\frac{1}{y}$

(D) $\frac{2(3y+2)}{3}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rational Expression Division" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite division as multiplication

Factor the denominator

Substitute and simplify

Answer: