question

evaluate $\frac{a^2 - b^2}{8ab^3}$ for $a = -2, b = 1$.

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Question

question

evaluate $\frac{a^2 - b^2}{8ab^3}$ for $a = -2, b = 1$.

provide your answer below:

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": [ "Evaluating Rational Expressions", "Fraction Arithmetic" ], "new_concepts": [], "current_concepts": [ "Evaluating Rational Expressions", "Fraction Arithmetic" ] } ## Identify the given values and expression Using the *Evaluating Rational Expressions* knowledge point $$ \begin{aligned} &\text{Expression: } \frac{a^2 - b^2}{8ab^3}\ &a = -2\ &b = 1 \end{aligned} $$ ## Substitute the values into the numerator Using the *Evaluating Rational Expressions* knowledge point $$ \begin{aligned} a^2 - b^2 &= (-2)^2 - (1)^2\ &= 4 - 1\ &= 3 \end{aligned} $$ ## Substitute the values into the denominator Using the *Evaluating Rational Expressions* knowledge point $$ \begin{aligned} 8ab^3 &= 8(-2)(1)^3\ &= -16(1)\ &= -16 \end{aligned} $$ ## Simplify the rational expression Using the *Fraction Arithmetic* knowledge point $$ \begin{aligned} \frac{a^2 - b^2}{8ab^3} &= \frac{3}{-16}\ &= -\frac{3}{16} \end{aligned} $$ Evaluate $\frac{a^2 - b^2}{8ab^3}$ for $a = -2, b = 1$. Provide your answer below: $-\frac{3}{16}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Evaluating Rational Expressions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and expression

Substitute the values into the numerator

Substitute the values into the denominator

Simplify the rational expression

Answer: