select the correct answer.

solve this equation.

$\frac{x+4}{6x} = \frac{1}{x}$

$\bigcirc$ $x = 0, 2$
$\bigcirc$ $x = -2$
$\bigcirc$ $x = 0, -2$
$\bigcirc$ $x = 2$

Question

select the correct answer.

solve this equation.

$\frac{x+4}{6x} = \frac{1}{x}$

$\bigcirc$ $x = 0, 2$
$\bigcirc$ $x = -2$
$\bigcirc$ $x = 0, -2$
$\bigcirc$ $x = 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Expressions", "Excluded Values" ], "new_concepts": [ "Rational Equations" ], "current_concepts": [ "Rational Expressions", "Excluded Values", "Rational Equations" ] } ## State the equation and identify the domain restrictions $$ \frac{x+4}{6x} = \frac{1}{x}, \quad x eq 0 $$ ## Solve the equation by cross-multiplying $$ \begin{aligned} x(x+4) &= 6x \ x^2 + 4x &= 6x \ x^2 - 2x &= 0 \ x(x-2) &= 0 \end{aligned} $$ ## Determine the valid solutions $$ \begin{aligned} x = 0 \quad &\text{or} \quad x = 2 \ x & eq 0 \implies x = 2 \end{aligned} $$

(A) $x = 0, 2$

(B) $x = -2$

(C) $x = 0, -2$

(D) $x = 2$

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

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QUESTION IMAGE

Question

Explanation:

State the equation and identify the domain restrictions

Solve the equation by cross-multiplying

Determine the valid solutions

Answer: