To divide by a fraction, multiply by its reciprocal.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Rewrite as .

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

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

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.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify ((75n^2-147)/(5n^2-12n+7))÷((35n^2+34n-21)/(n^2-8n+7))