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 quantity x plus 6.

X² - 3 x - 54 = x² + 6 x - 9 x - 54 = x (x + 6) - 9 (x + 6) = (x + 6) (x - 9)

x² - 18 x + 81 = (x - 9) ²

x² + 12 x + 36 = (x + 6) ²

... = (x + 6) · (x - 9) / (x - 9) ² * (x + 6) ² / (x + 6) = (after cancellation)

= (x + 6) ² / (x - 9)