find the excluded values in this rational expression.

\\frac{6x^2 - 5x + 2}{3x^2 + 13x + 12}\

\x \
eq ?, -\frac{\box}{\box}\

enter the smallest excluded value first.

Question

find the excluded values in this rational expression.

\\frac{6x^2 - 5x + 2}{3x^2 + 13x + 12}\

\x \
eq ?, -\frac{\box}{\box}\

enter the smallest excluded value first.

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": [ "Factoring Trinomials", "Excluded Values" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Excluded Values", "Simplifying Rational Expressions" ] } ## Identify the denominator Using the *Excluded Values* knowledge point $$ 3x^2 + 13x + 12 = 0 $$ ## Factor the quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &3x^2 + 9x + 4x + 12 = 0\ &3x(x + 3) + 4(x + 3) = 0\ &(3x + 4)(x + 3) = 0 \end{aligned} $$ ## Solve for the excluded values Using the *Excluded Values* knowledge point $$ \begin{aligned} &x + 3 = 0 \implies x = -3\ &3x + 4 = 0 \implies x = -\frac{4}{3} \end{aligned} $$ ## Order the values Using the *Excluded Values* knowledge point $$ \begin{aligned} &-3 < -\frac{4}{3}\ &\text{Smallest value: } -3\ &\text{Other value: } -\frac{4}{3} \end{aligned} $$ Find the excluded values in this rational expression. $$\frac{6x^2 - 5x + 2}{3x^2 + 13x + 12}$$ $x eq$ -3, $-\frac{4}{3}$ Enter the smallest excluded value first. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Excluded Values" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the denominator

Factor the quadratic trinomial

Solve for the excluded values

Order the values

Answer: