Question

question

divide: \frac{y^2 + y - 42}{y^2 - 36}.

provide your answer below:

Explanation:

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<reasoning>

Factor the numerator trinomial

Using the Factoring Trinomials knowledge point
\[
y^2 + y - 42 = (y + 7)(y - 6)
\]

Factor the denominator binomial

Using the Difference of Squares knowledge point
\[
y^2 - 36 = (y - 6)(y + 6)
\]

Simplify the rational expression

We divide the factored numerator by the factored denominator and cancel the common factor:
\[
\frac{y^2 + y - 42}{y^2 - 36} = \frac{(y + 7)(y - 6)}{(y + 6)(y - 6)} = \frac{y + 7}{y + 6} \quad (y
eq 6)
\]
</reasoning>

<answer>
Divide: \(\frac{y^2 + y - 42}{y^2 - 36}\).

Provide your answer below:
<blank>\(\frac{y + 7}{y + 6}\)</blank>
</answer>

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"Mathematics",
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"Simplifying Rational Expressions"
]
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</post_analysis>

Answer:

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<reasoning>

Factor the numerator trinomial

Using the Factoring Trinomials knowledge point
\[
y^2 + y - 42 = (y + 7)(y - 6)
\]

Factor the denominator binomial

Using the Difference of Squares knowledge point
\[
y^2 - 36 = (y - 6)(y + 6)
\]

Simplify the rational expression

We divide the factored numerator by the factored denominator and cancel the common factor:
\[
\frac{y^2 + y - 42}{y^2 - 36} = \frac{(y + 7)(y - 6)}{(y + 6)(y - 6)} = \frac{y + 7}{y + 6} \quad (y
eq 6)
\]
</reasoning>

<answer>
Divide: \(\frac{y^2 + y - 42}{y^2 - 36}\).

Provide your answer below:
<blank>\(\frac{y + 7}{y + 6}\)</blank>
</answer>

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"Mathematics",
"Algebra",
"Simplifying Rational Expressions"
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</post_analysis>