Question 234607
x +7/(x-2) <0
.
multiply  by  (x-2)
.
x(x-2) +7 <0
.
x^2 -2x +7 <0
.
solve  by  quadratic  formula
.
a=1,,,b--2,,,,c=7
.
x=[ -(-2)+/- sqrt{(-2)^2 -4(1) (7)}]/2(1)
.
x=[ 2 +/- sqrt{4-28}]/2
.
x= 1 +/- 2.45i,,,,,
.
returning  to  x^2 -2x +7<0
.
(x-1 -2.45i)(x-1+2.45i) <0
.
x-1-2.45i <0,,,,,x< 1+2.45i
.
x-1+2.45i <0,,,,,x< 1-2.45i
.