question 2 (1 point) saved

the expression $\frac{x^2 + 2x - 15}{x + 5}$ factors to $\frac{(x - 3)(x + 5)}{x + 5}$. even though this expression simplifies to $x - 3$, it still has the restriction $x \
eq -5$.

true
false

Question

question 2 (1 point) saved

the expression $\frac{x^2 + 2x - 15}{x + 5}$ factors to $\frac{(x - 3)(x + 5)}{x + 5}$. even though this expression simplifies to $x - 3$, it still has the restriction $x \
eq -5$.

true
false

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Simplifying Rational Expressions", "Domain of Rational Functions" ], "new_concepts": [], "current_concepts": [ "Simplifying Rational Expressions", "Domain of Rational Functions", "Restrictions on Rational Expressions" ] } ## Analyze the original expression and its domain Using the **Domain of Rational Functions** knowledge point $$ \begin{aligned} &f(x) = \frac{x^2+2x-15}{x+5}\ &\text{Denominator: } x+5 e 0 \implies x e -5 \end{aligned} $$ ## Simplify the expression Using the **Simplifying Rational Expressions** knowledge point $$ \begin{aligned} &f(x) = \frac{(x-3)(x+5)}{x+5}\ &f(x) = x-3,\quad x e -5 \end{aligned} $$ ## Evaluate the statement The statement asserts that even though the expression simplifies to $x-3$, it still has the restriction $x e -5$. Since the simplified function must preserve the domain of the original unsimplified expression, the restriction $x e -5$ remains. Therefore, the statement is True.

True

False

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

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Explanation:

Analyze the original expression and its domain

Simplify the expression

Evaluate the statement

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