question 10 (1 point)

when simplified, the expression $\frac{x^2 + x - 2}{x^2 - 3x + 2}$ is equal to $\frac{x - 2}{-3x + 2}$.

true
false

Question

question 10 (1 point)

when simplified, the expression $\frac{x^2 + x - 2}{x^2 - 3x + 2}$ is equal to $\frac{x - 2}{-3x + 2}$.

true
false

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Simplifying Rational Expressions" ], "current_concepts": [ "Simplifying Rational Expressions", "Factoring Quadratics" ] } ## Factor the numerator and denominator of the rational expression $$ \begin{aligned} \text{Numerator: } & x^2 + x - 2 = (x + 2)(x - 1) \ \text{Denominator: } & x^2 - 3x + 2 = (x - 2)(x - 1) \end{aligned} $$ ## Simplify the rational expression by canceling common factors $$ \frac{x^2 + x - 2}{x^2 - 3x + 2} = \frac{(x + 2)(x - 1)}{(x - 2)(x - 1)} = \frac{x + 2}{x - 2} \quad (x eq 1) $$ ## Compare the simplified expression with the given statement $$ \frac{x + 2}{x - 2} eq \frac{x - 2}{-3x + 2} $$

True

(B) False

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

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QUESTION IMAGE

Question

Explanation:

Factor the numerator and denominator of the rational expression

Simplify the rational expression by canceling common factors

Compare the simplified expression with the given statement

Answer: