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 .

Multiply and .

Multiply and .

Reorder the factors of .

Reorder the factors of .

Combine the numerators over the common denominator.

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 .

Add and .

Add and .

Simplify each term.

Multiply by .

Multiply by .

Apply the distributive property.

Multiply by .

Subtract from .

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