Уравнение с модулем|x+1/x+5|=x+1/x-5

Question

Уравнение с модулем
|x+1/x+5|=x+1/x-5

Answer 1

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