# How do you solve #x/(x-3)>0# using a sign chart?

##### 1 Answer

#### Explanation:

A rational function of the form

Thus, the function

When it changes signs can be solved by equating it to

#0# or finding when it is undefined. These are the only values where it can change signs. In order to know if it actually changes signs, look at two values, one larger and one smaller, and see if it actually changes signs.

For example, for#(x-3)^2(x-1)# , the only value which it can change signs is#x=3# and#x=1# . However, if you check the nearby values for#x=3# , you will find that the function still stays positive and does not change signs.

Thus, we can create a sign diagram for

From this sign diagram, we can see that

We can draw a graph to verify this answer:

graph{x/(x-3) [-10, 10, -5, 5]}