Ответы и объяснения

  • Voxman
  • главный мозг
2013-03-24T21:33:47+04:00

 

1) (3x - 6)x/(8x(x^2-4x+4)) = (3x - 6)/8(x^2-4x+4) =\\ 3(x-2)/8(x-2)^2 = 3/(8(x-2))\\\\ 2) (x^3+1)/(x^2-x+1) =\\ (x+1)(x^2-x+1)/(x^2-x+1) = (x+1)\\\\

 

 

3) 1/(x-1) >= -2\\ 1. \ (x-1>0, x>1)\\ 1 >= -2(x-1)\\ -1/2 =< (x-1)\\ 1/2 =< x\\2. \ (x-1<0, x<1)\\ 1 =< -2(x-1) \\ -1/2 >= (x-1)\\ 1/2 >= x\\ (x =< 1/2) \ and \ (x>1)\\\\4) x -3 + 4/(x+1) > 0\\ 1. \ ((x+1)>0, x>-1)\\4/(x+1) > 3 - x\\ 4 > (3-x)(x+1)\\ 4 > 3x + 3 -x^2 -x\\ 0 > -x^2 +2x -1\\ 0 < x^2-2x+1\\ 0 < (x-1)^2, \ x <> 1 \\2.\ ((x+1)<0, x<-1)\\ 4/(x+1) < 3 - x\\ 4 < (3-x)(x+1)\\ 4 < 3x + 3 -x^2 -x\\ 0 < -x^2 +2x -1\\ 0> x^2-2x+1\\ 0 > (x-1)^2

 

не при каких x. Решение:

 

(-1 < x < 1) \ and \ (x > 1)

 

 

 

5) 1/2x > 1/(1-x)\\1. \ (1-x > 0, x < 1)\\ a. \ (1-x)/2x-1 > 0 (2x > 0)\\ (1-x)-2x > 0\\ 1-3x > 0\\ -3x > -1\\ x < 1/3\\ b. \ (2x < 0)\\ (1-x)/2x-1 < 0\\ 1-3x < 0\\ -3x < -1\\ x > 1\3\\ 2. \  (1-x < 0, x > 1)\\ (1-x)/2x-1 < 0\\ a. \ (2x >0)\\(1-x)-2x < 0\\ 1-3x < 0\\ -3x < -1\\ x > 1/3\\ b. \ (2x < 0)\\ (1-x)-2x > 0\\ 1-3x > 0\\ -3x > -1\\ x < 1/3\\\\ (0<x<1/3) \ and \ (x >1)