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 .

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 .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify (z^2)/(z+1)*(z^2+3z+2)/(z^2+3z)