Вправи для повторення розділу 3 » 37 (1-3)

Скоротіть дріб: 1) (4x^2- 81)/(2x^2- 5x-18). 2x2 – 5x – 18 = 0; D = (–5)2 – 4 • 2 • (–18) = 169; x1 = (5+13)/4 = 18/4 = 4,5; x2 = (5-13)/4 = –2; (4x^2- 81)/(2x^2- 5x-18) = ((2x-9)(2x+9))/(2(x-4,5)(x+2)) = ((2x-9)(2x+9))/((2x-9)(x+2)) = (2x+9)/(x+2). 2) (2x^2+ 6x-20)/(x^3- 8). 2x2 + 6x – 20 = 0; D = 36 – 4 • 2 • (–20) = 196; x1 = (-6+14)/4 = 2; x2 = (-6-14)/4 = –5. (2x^2+ 6x-20)/(x^2- 8) = (2(x-2)(x+5))/((x-2)(x^2+ 2x+4)) = (2(x+5))/(x^2+ 2x+4). 3) (2x^2- 12x+18)/(〖2x〗^2- x-15). 2x2 – 12x + 18 = 0; D = (–12)2 – 4 • 2 • 18 = 0; x1 = x2 = 12/4 = 3. 2x2 – x – 15 = 0; D = (–1)2 – 4 • 2 • (–15) = 121; x1 = (1+11)/4 = 3; x2 = (1-11)/4 = –2,5. (2x^2- 12x+18)/(〖2x〗^2- x-15) = (2(x-3)^2)/(2(x-3)(x+2,5)) = (x-3)/(x+2,5).