Question

Х^2+2x+3/x-6x/х^2+2x+3=5

Answer 1

x≠0
y=(x²+2x+3)/x

y - (6/y)=5
y≠0

y² -5y-6=0
D=25+24=49
y₁=(5-7)/2=-1
y₂=(5+7)/2=6

При у= -1
(x²+2x+3)/x= -1
x²+2x+3=-x
x²+2x+x+3=0
x²+3x+3=0
D=9-12<0
нет решений.

При у=6
(x²+2x+3)/x=6
x²+2x+3=6x
x²+2x-6x+3=0
x²-4x+3=0
D=16-12=4
x₁=(4-2)/2=1
x₂=(4+2)/2=3

Ответ: 1;  3.