Сократить дробь: x^3-4x^2-9x+36/x^2-x+12

(x³ - 4 x² - 9 x + 36) / (x² - x - 12);

x² - x - 12 = 0;

D = 1 + 48 = 49;

x = (1 ± √49) : 2;

x = (1 + 7) : 2; x = 4;

x' = (1 - 7) : 2; x' = - 3;

(x³ - 4 x² - 9 x + 36) / (x² - x - 12) = [ (x³ - 4 x²) - (9 x - 36) ]/[ (x - 4) (x + 3) ] =

= [x² (x - 4) - 9 (x - 4) ]/[ (x - 4) (x + 3) ] = [ (x - 4) (x² - 9) ]/[ (x - 4) (x + 3) ] =

= [ (x - 4) (x - 3) (x + 3) ]/[ (x - 4) (x + 3) ] = x - 3.