Решение
2x/(2x - 1) - (x + 1)/(x + 2) = 4/(2 - 3x - 2x²)
2x/(2x - 1) - (x + 1)/(x + 2) + 4/(2x² + 3x - 2)
2x² + 3x - 2 = 0
D = 9 + 4*2*2 = 25
x1 = (-3 - 5)/4 = - 2
x2 = (-3 + 5)/4 = 1/2
2x² + 3x - 2 = 2(x + 2)*(2x - 1)
2x/(2x - 1) - (x + 1)/(x + 2) + 2/(x + 2)(2x - 1) = 0
[2x*(x + 2) - (x + 1)*(2x - 1) + 2] / [(x + 2)*(2x - 1)] = 0
(2x² + 4x - 2x² + x - 2x + 1 + 2) / [(x + 2)*(2x - 1)] = 0
(3x + 3) / [(x + 2)*(2x - 1)] = 0
3x + 3 = 0
3x = - 3
x = - 1
(x + 2)*(2x - 1 )≠ 0, x ≠ - 2, x ≠ 1/2
Ответ ч = - 1