solve the following rational equation.

\\frac{x}{x + 3} = \frac{8}{x - 2}\

$x = ?, \quad$

enter the smallest solution first.

Question

solve the following rational equation.

\\frac{x}{x + 3} = \frac{8}{x - 2}\

$x = ?, \quad$

enter the smallest solution first.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Rational Equations" ], "new_concepts": [], "current_concepts": [ "Rational Equations", "Solving Rational Equations", "Factoring Trinomials" ] } ## Identify excluded values $$ x e -3, \quad x e 2 $$ ## Cross-multiply to clear fractions $$ \begin{aligned} x(x - 2) &= 8(x + 3) \ x^2 - 2x &= 8x + 24 \end{aligned} $$ ## Rearrange into standard quadratic form and solve $$ \begin{aligned} x^2 - 10x - 24 &= 0 \ (x - 12)(x + 2) &= 0 \ x = 12 \quad &\text{or} \quad x = -2 \end{aligned} $$ Solve the following rational equation. $$\frac{x}{x + 3} = \frac{8}{x - 2}$$ $x =$ -2, 12 Enter the smallest solution first. { "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

Cross-multiply to clear fractions

Rearrange into standard quadratic form and solve

Answer: