Уравнение с модулем

|x+1/x+5|=x+1/x-5

1) x∈ (-≈; -5)

(x+1) / (x+5) = (x+1) / (x-5)

(x+1) (x-5) - (x+1) (x+5) = 0

(x+1) (x-5-x-5) = 0

-10 (x+1) = 0

x=-1∉ (-≈; -5)

2) x∈[-5; -1]

(x+1) / (x+5) = (x+1) / (5-x)

(x+1) (5-x) - (x+1) (x+5) = 0

(x+1) (5-x-x-5) = 0

-2x (x+1) = 0

x=0∉[-5; -1]

3) x∈ (-1; ≈)

(x+1) / (x+5) = (x+1) / (x-5)

(x+1) (x-5) - (x+1) (x+5) = 0

(x+1) (x-5-x-5) = 0

-10 (x+1) = 0

x=-1∉ (-1; ≈)

ответ х=-1