# Simplify ((a^2-14a+49)/(a^2-a-42))÷((a^2-49)/7)

To divide by a fraction, multiply by its reciprocal.
Factor using the perfect square rule.
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , 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 and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify terms.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Simplify ((a^2-14a+49)/(a^2-a-42))÷((a^2-49)/7)

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