current objective
simplify a rational expression with opposite factors

question
divide: $\frac{14m^2 - 11m - 60}{-12m^2 + 24m + 15}$.

provide your answer below:

Question

current objective
simplify a rational expression with opposite factors

question
divide: $\frac{14m^2 - 11m - 60}{-12m^2 + 24m + 15}$.

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Trinomial Factorization", "Greatest Common Factor Factoring", "Opposite Factors", "Simplifying Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Trinomial Factorization", "Greatest Common Factor Factoring", "Opposite Factors", "Simplifying Rational Expressions" ] } ## Factor the numerator trinomial Using the **Trinomial Factorization** knowledge point $$ \begin{aligned} 14m^2 - 11m - 60 &= 14m^2 - 35m + 24m - 60 \ &= 7m(2m - 5) + 12(2m - 5) \ &= (2m - 5)(7m + 12) \end{aligned} $$ ## Factor the denominator trinomial Using the **Greatest Common Factor Factoring** and **Trinomial Factorization** knowledge points $$ \begin{aligned} -12m^2 + 24m + 15 &= -3(4m^2 - 8m - 5) \ &= -3(4m^2 - 10m + 2m - 5) \ &= -3[2m(2m - 5) + 1(2m - 5)] \ &= -3(2m - 5)(2m + 1) \end{aligned} $$ ## Simplify the rational expression Using the **Simplifying Rational Expressions** knowledge point $$ \begin{aligned} \frac{14m^2 - 11m - 60}{-12m^2 + 24m + 15} &= \frac{(2m - 5)(7m + 12)}{-3(2m - 5)(2m + 1)} \ &= \frac{7m + 12}{-3(2m + 1)} \ &= -\frac{7m + 12}{3(2m + 1)} \end{aligned} $$ $-\frac{7m + 12}{3(2m + 1)}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the numerator trinomial

Factor the denominator trinomial

Simplify the rational expression

Answer: