ГДЗ Алгебра 9 клас Істер НУШ

82. Скоротіть дроби:

1) (x^2 - x - 6)/(2x + 4) = ((x - 3)(x + 2))/(2(x + 2)) = (x - 3)/2;
x2 – x – 6 = (x – 3)(x + 2);
x1 + x2 = 1; x1 • x2 = –6;
x1 = 3; x2 = –2.
2) (〖3x〗^2 - 8x - 3)/(x^2 - 9) = ((3x + 1)(x - 3))/((x - 3)(x + 3)) = (3x + 1)/(x + 3);
3x2 – 8x – 3 = 3(x + 1/3)(x – 3) = (3x + 1)(x – 3);
D = (–8)2 – 4 • 3 • (–3) = 64 + 36 = 100;
x1 = (8 - √100)/(2 • 3) = (8 - 10)/6 = (-2)/6 = –1/3.
x2 = (8 + 10)/6 = 18/6 = 3.