select all the correct answers.

which factors compose the least common denominator for this difference?

\\frac{11x}{x^2 + 4x - 12} - \frac{7}{2x^2 - 4x}\

- $(x + 2)$
- $(x - 6)$
- $(x + 6)$
- $(x - 4)$
- $2x$
- $(x - 2)$

Question

select all the correct answers.

which factors compose the least common denominator for this difference?

\\frac{11x}{x^2 + 4x - 12} - \frac{7}{2x^2 - 4x}\

- $(x + 2)$
- $(x - 6)$
- $(x + 6)$
- $(x - 4)$
- $2x$
- $(x - 2)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Rational Expressions" ], "new_concepts": [ "Least Common Denominator" ], "current_concepts": [ "Factoring Quadratics", "Rational Expressions", "Least Common Denominator" ] } ## Factor the denominators of both rational expressions $$ \begin{aligned} x^2 + 4x - 12 &= (x + 6)(x - 2) \ 2x^2 - 4x &= 2x(x - 2) \end{aligned} $$ ## Determine the least common denominator (LCD) $$ \text{LCD} = 2x(x + 6)(x - 2) $$ ## Identify the matching factors from the given options $$ \text{Factors of the LCD: } 2x, \quad (x + 6), \quad (x - 2) $$

(x + 2)

(x - 6)

(x + 6)

(x - 4)

2x

(x - 2)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Least Common Denominator" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Factor the denominators of both rational expressions

Determine the least common denominator (LCD)

Identify the matching factors from the given options

Answer: