Ответы и объяснения

  • Minsk00
  • почетный грамотей
2014-01-15T15:12:08+04:00
1/(2-x) -1 =1/(x-2) -(6-x)/(3x²-12)
ОДЗ:
x-2 =/= 0
x=/=2
3x²-12 ≠ 0
3*(x²-4) ≠0
(x-2)(x+2) ≠0
x+2 =/=0
x=/=-2

1/(x-2) - (6-x)/(3(x²-4)) -1/(2-x) + 1 = 0
1/(x-2)+1/(x-2) + (x-6)/(3(x-2)(x+2)) +1 = 0
2/(x-2) + (x-6)/(x-6)/(3(x-2)(x+2)) +1 = 0
(2*3(x+2) + x - 6 + 3(x-2)(x+2))/(3(x-2)(x+2)) = 0
( 6x +12 +x - 6 + 3x² -12)/(3(x-2)(x+2)) = 0
(3x² + 7x - 6)/(3(x-2)(x+2)) = 0
3x² + 7x - 6 = 0
D =49+72 =121
x1 = (-7-11)/6 = -3
x2 =(-7+11)/6 = 2/3
Ответ: -3; 2/3