Question

Решите уравнение:
(2х-1)(х+1) (3х+1)(х-2)
————— - ————— =-2
2 3

Answer 1

$\frac{(2x - 1)(x + 1)}{2} - \frac{(3x + 1)(x - 2)}{3} = - 2 \\ \frac{3(2x - 1)(x + 1) - 2(3x + 1)(x - 2)}{6} = - 2 \: \: \: \: \: | \times 6 \\ 3(2 {x}^{2} + 2x - x - 1) - 2(3 {x}^{2} - 6x + x - 2) = - 12 \\ 6 {x}^{2} + 3x - 3 - 6 {x}^{2} + 10x + 4 = - 12 \\ 13x = - 12 - 1 \\ 13x = - 13\: \: \: \: \: | \div 13 \\ x = - 1$
Проверим:

$\frac{(2 \times ( - 1) - 1)( - 1+ 1)}{2} - \frac{(3 \times ( - 1) + 1)( - 1 - 2)}{3} = - 2 \\ \frac{ - 3 \times 0}{2} - \frac{ - 2 \times ( - 3)}{3} = - 2 \\ - \frac{6}{3} = - 2 \\ - 2 = - 2$