1/x-3<-1 find all the factor

Answer 1

1/(x-3) < -1

what do you mean factors? You want a solution set

If x-3 > 0, then
1 < 3-x
x < 2
Not possible if x>3

If x-3 < 0 or x < 3, then
1 > 3-x
x > 2

So, the only solutions are 2<x<3

verify here:

http://www.wolframalpha.com/input/?i=1%2F%28x-3%29+%3C+-1+for+-5%3Cx%3C5