X^2 - 8x - 9 over x^2 - 1

Factor both equations, you'll get (x-9) (x+1) for the first one and (x+1) (x-1) for the second one.

new equation: (x-9) (x+1) over (x+1) (x-1). You can cancel out both (x+1) s because when divided by each other you're left with the number one. The answer is (x-9) over (x-10