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.

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Multiply and .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Add and .

Add and .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify 1/(x+2)+1/(x+3)+1/(x^2+5x+6)