Simplify

(n^2-10n+24) / (n^2-13n+42) - 9 / (n-7)

Factor the numerator and denominator of the first fraction ...

(n^2-6n-4n+24) / (n^2-6n-7n+42)

(n (n-6) - 4 (n-6)) / (n (n-6) - 7 (n-6))

((n-4) (n-6)) / ((n-7) (n-6)), note that the (n-6) s cancel out leaving:

(n-4) / (n-7) so now the equation looks like:

(n-4) / (n-7) - 9 / (n-7) since they now have a common denominator ...

(n-4-9) / (n-7) which is

(n-13) / (n-7)