simplify the following rational expression.

\\frac{2x - 6}{x^2 + x - 12}\

\\frac{?}{x + }\

Question

simplify the following rational expression.

\\frac{2x - 6}{x^2 + x - 12}\

\\frac{?}{x +  }\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Rational Expressions", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Simplifying Rational Expressions", "Factoring Trinomials" ] } ## Factor the numerator and denominator $$ \begin{aligned} 2x - 6 &= 2(x - 3) \ x^2 + x - 12 &= (x - 3)(x + 4) \end{aligned} $$ ## Cancel the common factor $$ \begin{aligned} \frac{2x - 6}{x^2 + x - 12} &= \frac{2(x - 3)}{(x - 3)(x + 4)} \ &= \frac{2}{x + 4} \quad (x eq 3) \end{aligned} $$ ## Identify the missing values $$ \begin{aligned} \text{Numerator } [?] &= 2 \ \text{Denominator constant } [ ] &= 4 \end{aligned} $$ Simplify the following rational expression. $$\frac{2x - 6}{x^2 + x - 12}$$ The simplified expression is $\frac{2}{x + 4}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the numerator and denominator

Cancel the common factor

Identify the missing values

Answer: