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

To divide by a fraction, multiply by its reciprocal.
Factor using the AC method.
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.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Factor using the AC method.
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 .
Cancel the common factor.
Rewrite the expression.
Multiply .
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.