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)