question

solve: $\frac{1}{x - 1} = \frac{2}{3x}$.

provide your answer below:

$x = \square$

Question

question

solve: $\frac{1}{x - 1} = \frac{2}{3x}$.

provide your answer below:

$x = \square$

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": [ "Domain of Rational Functions", "Solving Linear Equations" ], "new_concepts": [ "Solving Rational Equations" ], "current_concepts": [ "Domain of Rational Functions", "Solving Linear Equations", "Solving Rational Equations" ] } ## Identify excluded values Using the *Domain of Rational Functions* knowledge point $$ \begin{aligned} &x - 1 e 0 \implies x e 1\ &3x e 0 \implies x e 0 \end{aligned} $$ ## Clear the denominators Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &1 \cdot (3x) = 2 \cdot (x - 1)\ &3x = 2x - 2 \end{aligned} $$ ## Solve for x Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &3x - 2x = -2\ &x = -2 \end{aligned} $$ ## Verify the solution Using the *Domain of Rational Functions* knowledge point $$ \begin{aligned} &x = -2 otin \{0, 1\} \end{aligned} $$ Solve: $\frac{1}{x - 1} = \frac{2}{3x}$. Provide your answer below: $x =$ $-2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify excluded values

Clear the denominators

Solve for x

Verify the solution

Answer: