To divide by a fraction, multiply by its reciprocal.

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

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

Cancel the common factor.

Rewrite the expression.

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.

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify ((m^2-m)/(m^2-1))÷((m+11)/(m^2+12m+11))