Упростите выражение: x^3-x^2-x+1/x^4-x^3-3x^2+5x-2

(x^3 - x^2 – x + 1)/(x^4 - x^3 - 3x^2 + 5x – 2) ==(( x^3 - x^2) + (– x + 1))/(( x^4 - x^3) + ((- 3x^2 + 5x – 2)) == ((x^2*(x – 1) – (x – 1))/((x^3*(x – 1) + ((x – 1)(-3x + 2)) = = ((x – 1)(x^2 – 1))/((x – 1)(x^3 – 3x + 2)) == (x^2 – 1))/(x^3 – 3x + 2).(- 3x^2 + 5x – 2) = (x – 1)(-3x + 2) – получили путем разложения квадратного трехчлена на множители:- 3x^2 + 5x – 2 = 0;D = b^2 – 4ac;D = 25 – 4*(-3)*(-2) = 25 – 24 = 1; √D = 1;x = (-b ± √D)/(2a);x1 = (-5 + 1)/(-6) = 4/6 = 2/3;x2 = (-5 - 1)/(-6) = 6/6 = 1;ax^2 + bx + c = a(x – x1)(x – x2);(- 3x^2 + 5x – 2) = -3(x - 2/3)(x – 1) = (-3x + 2)(x – 1).Ответ. (x^2 – 1))/(x^3 – 3x + 2).