ГДЗ Алгебра 9 клас Істер НУШ

81. Скоротіть дроби:

1) (4x - 12)/(x^2 - 2x - 3) = (4(x - 3))/((x - 3)(x + 1)) = 4/(x + 1).
x2 – 2x – 3 = (x – 3)(x + 1);
x1 + x2 = 2; x1 • x2 = –3.
x1 = 3; x2 = –1.
2) (x^2 - 4)/(〖2x〗^2 - 5x + 2) = ((x - 2)(x + 2))/((2x - 1)(x - 2)) = (x + 2)/(2x - 1).
2x2 – 5x + 2 = 2(x – 1/2)(x – 2) = (2x – 1)(x – 2).
D = (–5)2 – 4 • 2 • 2 = 25 – 16 = 9.
x1 = (5 - √9)/(2 • 2) = (5 - 3)/4 = 2/4 = 1/2;
x2 = (5 + √9)/(2 • 2) = (5 + 3)/4 = 8/4 = 2.