Вправи 1001 - 1100 » 1096 (б)

б) 2/(х^( 2)+ 3х+2) – х/(х^2- 1) + (5х+4)/(х^2+ х-2) = 0; x2 + 3x + 2 = (x + 1)(x + 2); x1 + x2 = –3; x1 • x2 = 2; x1 = –1; x2 = –2; x2 + x – 2 = (x + 2)(x – 1); x1 + x2 = –1; x1 • x2 = –2; x1 = –2; x2 = 1. 2^(\x-1)/((x+1)(x+2)) – x^(\x+2)/((x-1)(x+1)) + 〖5x+4〗^(\x+1)/((x+2)(x-1)) = 0; (2x-2- x^2-2x+5x^2+5x+4x+4)/((x+1)(x+2)(x-1)) = 0 (x(x + 1)(x + 2)(x – 1)); ОДЗ: x ≠ –1; x ≠ –2; x ≠ 1. 4x2 + 9x + 2 = 0; D = 92 – 4 • 4 • 2 = 81 – 32 = 49 = 72; x1 = (-9-7)/8 = (-16)/8 = –2 – не задовольняє ОДЗ; x2 = (-9+7)/8 = (-2)/8 = –1/4 = –0,25. Відповідь: –0,25.