What is x^2-9 divided by x^2-2x-15 in simplest form?

a^2 - b^2 ≡ (a + b)(a - b)

(x^2 - 9)/(x^2 - 2x - 15)
= (x^2 - 3^2)/(x^2 + 3x - 5x - 15)
= [(x + 3)(x - 3)]/[(x^2 + 3x) - (5x + 15)]
= [(x + 3)(x - 3)]/[x(x + 3) - 5(x + 3)]
= [(x + 3)(x - 3)]/[(x + 3)(x - 5)]
= (x - 3)/(x - 5)

(x+3)(x-3) / (x-5)(x+3)
=(x-3)/(x-5)

(x^2-9) is (x+3)(x-3) and (x^2-2x-15) is (x-5)(x+3). You can check to see I did this right by appling the FOIL method. Check out my Math Variety blog posts about the FOIL method for an explanation of what it is, practice problems, and solutions. Click on ads/links of interest and use my search box.
http://mathvariety.blogspot.com/2009/04/foil-method.html
http://mathvariety.blogspot.com/2009/05/foil-method-practice-problems.html
http://mathvariety.blogspot.com/2009/05/foil-method-solutions-to-practice.html


We have:
[(x+3)(x-3)]/[(x-5)(x+3)}

The (x+3)'s cancel out, and the answer is (x-3)/(x-5).

(x+3)(x-3)/(x-5)(x+3) = (x-3)/(x-5)
Is that as simple as it gets? I'm unsure.

=(x-3)(x+3)/(x-5)(x+3)=(x-3)/(x-5)

2/(x-5)+1