To divide by a fraction, multiply by its reciprocal.

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 .

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.

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

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)