Simplify the expression completely if possible. (x^2+7x+12)/(x^2)-9

To simplify the expression , we need to factor both the numerator and the denominator.First, let's factor the numerator :We look for two numbers that multiply to 12 and add up to 7. These numbers are 3 and 4.So, we can factor the numerator as: Next, let's factor the denominator :This is a difference of squares, which can be factored as: Now, we can rewrite the original expression using these factored forms: We see that \((x + 3)\) is a common factor in both the numerator and the denominator. We can cancel this common factor: Thus, the simplified form of the expression is: Note: The simplification is valid as long as and because these values would make the original denominator zero, which is undefined.