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.

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 .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify (x^2+5x+4)/(x^2+2x+1)*(2x+2)/(x+4)