current objective
find the least common denominator of rational expressions

question
find the lcd for $\frac{6}{2w^2 - 6w - 20}, \frac{6w}{2w^2 - 14w - 36}$.

provide your answer below:

Question

current objective
find the least common denominator of rational expressions

question
find the lcd for $\frac{6}{2w^2 - 6w - 20}, \frac{6w}{2w^2 - 14w - 36}$.

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", "Factoring Trinomials", "Least Common Denominator" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor Factoring", "Factoring Trinomials", "Least Common Denominator" ] } ## Factor the first denominator Using the *Greatest Common Factor Factoring* and *Factoring Trinomials* knowledge points $$ \begin{aligned} 2w^2 - 6w - 20 &= 2(w^2 - 3w - 10) \ &= 2(w - 5)(w + 2) \end{aligned} $$ ## Factor the second denominator Using the *Greatest Common Factor Factoring* and *Factoring Trinomials* knowledge points $$ \begin{aligned} 2w^2 - 14w - 36 &= 2(w^2 - 7w - 18) \ &= 2(w - 9)(w + 2) \end{aligned} $$ ## Determine the least common denominator Using the *Least Common Denominator* knowledge point $$ \begin{aligned} \text{LCD} &= 2 \cdot (w - 5) \cdot (w + 2) \cdot (w - 9) \ &= 2(w - 5)(w + 2)(w - 9) \end{aligned} $$ Find the LCD for $\frac{6}{2w^2 - 6w - 20}, \frac{6w}{2w^2 - 14w - 36}$. Provide your answer below: $2(w - 5)(w + 2)(w - 9)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Denominator" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the first denominator

Factor the second denominator

Determine the least common denominator

Answer: