[latex] \frac{2x-2}{x+2}+ \frac{x+3}{x-3}-5=0 [/latex] Решите уравнение Ответ: 1

ОДЗ x ≠ 3; x ≠ - 2; (2x - 2)(x - 3) + (x + 3)(x + 2) - 5(x + 2)(x - 3) = 0  2x^2 - 6x - 2x + 6 + x^2 + 5x + 6 - 5 (x^2 - x - 6) = 0  3x^2 - 3x + 12 - 5x^2 + 5x + 30 = 0  - 2x^2 +2x +  42 = 0   // : ( - 2) 2x^2 - 2x - 42 = 0  x^2 - x - 21 = 0  D = 1 + 4*21 = 85 x1 = ( 1  +√85)/2 = 1/2 + √85/2; x2 = ( 1 - √85)/2 = 1/2 - √85/2; x1 + x2 = 1/2 + √85/2 + 1/2 - √85/2 = 1;