question

divide: \frac{3b^2 - 12b + 12}{6b^2 - 24}

provide your answer below:

Question

question

divide: \frac{3b^2 - 12b + 12}{6b^2 - 24}

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor Factoring", "Perfect Square Trinomials", "Difference of Squares", "Simplifying Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor Factoring", "Perfect Square Trinomials", "Difference of Squares", "Simplifying Rational Expressions" ] } ## Factor the numerator Using the *Greatest Common Factor Factoring* and *Perfect Square Trinomials* knowledge points $$ \begin{aligned} 3b^2 - 12b + 12 &= 3(b^2 - 4b + 4) \ &= 3(b - 2)^2 \end{aligned} $$ ## Factor the denominator Using the *Greatest Common Factor Factoring* and *Difference of Squares* knowledge points $$ \begin{aligned} 6b^2 - 24 &= 6(b^2 - 4) \ &= 6(b - 2)(b + 2) \end{aligned} $$ ## Simplify the rational expression Using the *Simplifying Rational Expressions* knowledge point $$ \begin{aligned} \frac{3b^2 - 12b + 12}{6b^2 - 24} &= \frac{3(b - 2)^2}{6(b - 2)(b + 2)} \ &= \frac{3(b - 2)(b - 2)}{6(b - 2)(b + 2)} \ &= \frac{b - 2}{2(b + 2)} \end{aligned} $$ Divide: $\frac{b - 2}{2(b + 2)}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the numerator

Factor the denominator

Simplify the rational expression

Answer: