2+log(1/3)x2+3x/x-1=0

Question

2+log(1/3)x2+3x/x-1=0

Answer 1

ОДЗ
(x(x+3)/(x-1)>0
x=0  x=-3  x=1
           _                  +                _                  +
--------------(-3)-------------(0)--------------(1)--------------
x∈(-3;0) U (1;∞)
log(1/3)[(x²+3x)/(x-1)]=-2
(x²+3x)/(x-1)=9
x²+3x-9x+9=0
x²-6x+9=0
(x-3)²=0
x-3=0
x=3