Question

question

divide: \frac{3b^2 - 12b + 12}{6b^2 - 24}

provide your answer below:

Explanation:

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<reasoning>

Factor the numerator

Using the Greatest Common Factor Factoring and Perfect Square Trinomials knowledge points
\[

$$\begin{aligned} 3b^2 - 12b + 12 &= 3(b^2 - 4b + 4) \\ &= 3(b - 2)^2 \end{aligned}$$

\]

Factor the denominator

Using the Greatest Common Factor Factoring and Difference of Squares knowledge points
\[

$$\begin{aligned} 6b^2 - 24 &= 6(b^2 - 4) \\ &= 6(b - 2)(b + 2) \end{aligned}$$

\]

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point
\[

$$\begin{aligned} \frac{3b^2 - 12b + 12}{6b^2 - 24} &= \frac{3(b - 2)^2}{6(b - 2)(b + 2)} \\ &= \frac{3(b - 2)(b - 2)}{6(b - 2)(b + 2)} \\ &= \frac{b - 2}{2(b + 2)} \end{aligned}$$

\]
</reasoning>

<answer>
Divide: <blank>\(\frac{b - 2}{2(b + 2)}\)</blank>
</answer>

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Answer:

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<reasoning>

Factor the numerator

Using the Greatest Common Factor Factoring and Perfect Square Trinomials knowledge points
\[

$$\begin{aligned} 3b^2 - 12b + 12 &= 3(b^2 - 4b + 4) \\ &= 3(b - 2)^2 \end{aligned}$$

\]

Factor the denominator

Using the Greatest Common Factor Factoring and Difference of Squares knowledge points
\[

$$\begin{aligned} 6b^2 - 24 &= 6(b^2 - 4) \\ &= 6(b - 2)(b + 2) \end{aligned}$$

\]

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point
\[

$$\begin{aligned} \frac{3b^2 - 12b + 12}{6b^2 - 24} &= \frac{3(b - 2)^2}{6(b - 2)(b + 2)} \\ &= \frac{3(b - 2)(b - 2)}{6(b - 2)(b + 2)} \\ &= \frac{b - 2}{2(b + 2)} \end{aligned}$$

\]
</reasoning>

<answer>
Divide: <blank>\(\frac{b - 2}{2(b + 2)}\)</blank>
</answer>

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