question 4 (1 point)

when fully simplified, excluding restrictions, $\frac{3x+1}{x^2-4} \times \frac{x-2}{3x+1}$ is equal to

a) $\frac{1}{x+2}$

b) $\frac{x-2}{x^2-4}$

c) $\frac{1}{x-2}$

d) $x+2$

Question

question 4 (1 point)

when fully simplified, excluding restrictions, $\frac{3x+1}{x^2-4} \times \frac{x-2}{3x+1}$ is equal to

a) $\frac{1}{x+2}$

b) $\frac{x-2}{x^2-4}$

c) $\frac{1}{x-2}$

d) $x+2$

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": [ "Multiplying Rational Expressions", "Simplifying Rational Expressions" ], "new_concepts": [], "current_concepts": [ "Multiplying Rational Expressions", "Simplifying Rational Expressions" ] } ## Write the multiplication expression Using the *Multiplying Rational Expressions* knowledge point $$ \frac{3x+1}{x^2-4} \times \frac{x-2}{3x+1} = \frac{(3x+1)(x-2)}{(x^2-4)(3x+1)} $$ ## Factor the denominator and simplify Using the *Simplifying Rational Expressions* knowledge point $$ \begin{aligned} x^2-4 &= (x-2)(x+2)\ \frac{(3x+1)(x-2)}{(x-2)(x+2)(3x+1)} &= \frac{1}{x+2} \end{aligned} $$

(A) $\frac{1}{x+2}$

(B) $\frac{x-2}{x^2-4}$

(C) $\frac{1}{x-2}$

(D) $x+2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Write the multiplication expression

Factor the denominator and simplify

Answer: