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

To divide by a fraction, multiply by its reciprocal.
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.
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 .
Cancel the common factor.
Rewrite the expression.
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 out of .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Split the fraction into two fractions.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide ((z^2+11z+18)/(z^2+14z+45))÷((z^2+2z)/(z^2+10z+25))

Scroll to top