Your statemtent is incomplete.
I found the samestatment with the complete words: Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus 36 over x plus 6
Given that your goal is to learn an be able to solve any similar problem, I can teach you assuming that what I found is exactly what you need.
x^2 - 3x - 54 x^2 + 12x + 36
------------------ x ---------------------
x^2 - 18x + 81 x + 6
factor x^2 - 3x - 54 => (x - 9)(x + 6)
factor x^2 - 18x + 81 => (x - 9)^2
factor x^2 + 12x + 36 = (x + 6)^2
Now replace the polynomials with the factors=>
(x - 9) (x + 6) (x + 6)^2 (x + 6)^2 x^2 + 12x + 36
------------------------------ = --------------- = --------------------
(x - 9)^2 (x + 6) (x - 9) x - 9