Question

question

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

provide your answer below:

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} \frac{a^2 - b^2}{8ab^3} &= \frac{3}{-16}\\ &= -\frac{3}{16} \end{aligned}$$

\]
</reasoning>

<answer>
Evaluate \(\frac{a^2 - b^2}{8ab^3}\) for \(a = -2, b = 1\).

Provide your answer below:
<blank>\(-\frac{3}{16}\)</blank>
</answer>

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"Mathematics",
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"Evaluating Rational Expressions"
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</post_analysis>

Answer:

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<reasoning>

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
\[

$$\begin{aligned} \frac{a^2 - b^2}{8ab^3} &= \frac{3}{-16}\\ &= -\frac{3}{16} \end{aligned}$$

\]
</reasoning>

<answer>
Evaluate \(\frac{a^2 - b^2}{8ab^3}\) for \(a = -2, b = 1\).

Provide your answer below:
<blank>\(-\frac{3}{16}\)</blank>
</answer>

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"Mathematics",
"Algebra",
"Evaluating Rational Expressions"
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