find the excluded values in this rational expression.

\\frac{8x^2 - 5x + 7}{x^2 - 6x - 27}\

$x \
eq ?, $

enter the smallest excluded value first.

Question

find the excluded values in this rational expression.

\\frac{8x^2 - 5x + 7}{x^2 - 6x - 27}\

$x \
eq ?,  $

enter the smallest excluded value first.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Excluded Values", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Excluded Values", "Factoring Trinomials", "Simplifying Rational Expressions" ] } ## Set the denominator to zero $$ x^2 - 6x - 27 = 0 $$ ## Factor the quadratic equation $$ (x - 9)(x + 3) = 0 $$ ## Solve for the excluded values $$ \begin{aligned} x - 9 = 0 &\implies x = 9 \ x + 3 = 0 &\implies x = -3 \end{aligned} $$ Find the excluded values in this rational expression. $$\frac{8x^2 - 5x + 7}{x^2 - 6x - 27}$$ $x eq$ -3, 9 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:

Set the denominator to zero

Factor the quadratic equation

Solve for the excluded values

Answer: