Question

(1/(x-1))+(3/(|x|+1))>=(1/(|x|-1))

Answer 1

(1/(x-1))+(3/(|x|+1))>=(1/(|x|-1))

ОДЗ x≠ 1 x≠-1

1. x>=0

(1/(x-1))+(3/(x+1))>=(1/(x-1))

(3/(x+1))>= 0

для всех x>0 кроме 1

2. x<0

1/(x-1) + 3/(-x+1) >= 1/(-x-1)

2/(1 - x) + 1/(x+1) >= 0

(2x+ 2 + 1-x)/(1-x)(1+x) >=0

(x + 3)/(1-x)(1+x) >=0

(x+3)(x-1)(x+1) <=0

-----------[-3] ++++++++ (-1) ------------ (1) ++++++++++

x ∈ (-∞  -3] U (-1  1)     x<0

x∈ (-∞ -3] U (-1  0)

объединяем с первым

x∈ (-∞ - 3] U (-1  1) U (1 +∞)