# Subtract (y+3)/(y^2+7y+12)-5/(y^2-9)

Simplify each term.
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.
Simplify the denominator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply and .
Reorder the factors of .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Combine the opposite terms in .
Reorder the factors in the terms and .