Simplify ((a^2+7a+12)/(a^2-9))÷((a^2-7a+12)/(a^2-16))

Math
To divide by a fraction, multiply by its reciprocal.
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Simplify the denominator.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply .
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify ((a^2+7a+12)/(a^2-9))÷((a^2-7a+12)/(a^2-16))
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