Question

How do you solve `x/(x-3)>0`?

Answer 1

`f(x) >0` for `(-oo, 0] uu [3, +oo)`

Explanation:

`f(x) = x/(x-3)`

`:. f(x) <= 0` for `0<=x<3`

Hence `f(x)>0` for `(-oo, 0] uu [3, +oo)`

NB: `f(x)` is undefined at `x=3`

This can be seen from the graph of `f(x)` below.

graph{x/(x-3) [-16.02, 16.02, -8, 8.02]}