(3x-5)/(x-5)> =0
how do i get the answers for this problem?

> 0 

First, note that x is undefined at 5. / x ≠ 5
Second, replace the inequality sign with an equal sign so that we can solve it like a normal equation. / Your problem should look like:  = 0
Third, multiply both sides by x - 5. / Your problem should look like: 3x - 5 = 0
Forth, add 5 to both sides. / Your problem should look like: 3x = 5
Fifth, divide both sides by 3. / Your problem should look like: x = 
Sixth, from the values of x above, we have these 3 intervals to test: 
x < 
< x < 5
x > 5
Seventh, pick a test point for each interval. 

1. For the interval x <  :
Let's pick x - 0. Then,  > 0
After simplifying, we get 1 > 0 which is true.
Keep this interval.

2. For the interval  < x < 5:
Let's pick x = 2. Then,  > 0
After simplifying, we get -0.3333 > 0, which is false.
Drop this interval.

3. For the interval x > 5:
Let's pick x = 6. Then,  > 0
After simplifying, we get 13 > 0, which is ture.
Keep this interval.
Eighth, therefore, x <  and x > 5

x <  and x > 5