Вправи 1001 - 1100 » 1096 (в)

в) 1/(x-1) + 3/(x^2+ 9x+18) = (2x+5)/(x^2+ 5x-6); x2 + 9x + 18 = (x + 3)(x + 6); x1 + x2 = –9; x1 • x2 = 18; x1 = –3; x2 = –6; x2 + 5x – 6 = (x + 6)(x – 1); x1 + x2 = –5; x1 • x2 = –6; x1 = –6; x2 = 1. 1/(x-1) + 3/((x+3)(x+6)) = (2x+5)/((x+6)(x-1)); 1^(\\(x+3)(x+6))/(x-1) + 3^(\x-1)/((x+3)(x+6)) – 〖2x+5〗^(\x+3)/((x+6)(x-1)) = 0; (x^2+6x+3x+18+3x-3-(〖2x〗^2+ 6x+5x+15))/((x- 1)(x+3)(x+6)) = 0; (x(x – 1)(x + 3)(x + 6)); ОДЗ: x ≠ 1; x ≠ –3; x ≠ –6. x2 + 12x + 15 – 2x2 – 11x – 15 = 0; –x2 + x = 0; x(1 – x) = 0; x = 0 або 1 – x = 0; x = 1 – не задовольняє ОДЗ. Відповідь: 0.