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:

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