To divide by a fraction, multiply by its reciprocal.

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.

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.

Rewrite the expression.

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 out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Split the fraction into two fractions.

Cancel the common factor.

Divide by .

Divide ((z^2+11z+18)/(z^2+14z+45))÷((z^2+2z)/(z^2+10z+25))