solve the inequality
x+3/x-2 less then or equal to 0
suspect you mean
(x+3) / (x-2) </= 0
first let's look at the singularity when x = 2
when x is a little above 2 we have 5/+0
which is +oo
when x is a little below 2 we have 5/-0 which is -oo
so to the right of x = 2 it is +, no matter how big x gets
to the left of x = 2, it is -
until x = -3
then it is zero
to the left of x = -3, it is + again
SO
it is only - between x = -3 and x = 2
-3 </= x </= +2