solve the following rational equation.

\\frac{x}{x + 3} = \frac{6}{x - 1}\

$x = ?, \quad$

enter the smallest solution

Question

solve the following rational equation.

\\frac{x}{x + 3} = \frac{6}{x - 1}\

$x = ?, \quad$

enter the smallest solution

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rational Equations", "Solving Rational Equations" ], "new_concepts": [], "current_concepts": [ "Rational Equations", "Solving Rational Equations" ] } ## Identify excluded values $$ x e -3, \quad x e 1 $$ ## Clear denominators by cross-multiplying $$ \begin{aligned} x(x - 1) &= 6(x + 3) \ x^2 - x &= 6x + 18 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} x^2 - 7x - 18 &= 0 \ (x - 9)(x + 2) &= 0 \ x = 9 \quad \text{or} \quad x = -2 \end{aligned} $$ Solve the following rational equation. $$\frac{x}{x + 3} = \frac{6}{x - 1}$$ $x =$ $-2$, $9$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify excluded values

Clear denominators by cross-multiplying

Solve the quadratic equation

Answer: