Question

Which graph shows the solution set of ​

Answer 1

Hence final answer is
`(1,3)`.

correct choice is D because both ends are open circles.

Explanation:

Given inequality is
`(x-1)/(x-3)<0`

Setting both numerator and denominator =0 gives:

x-1=0, x-3=0

or x=1, x=3

Using these critical points, we can divide number line into three sets:

`(-\infty,1)`,
`(1,3)` and
`(3,\infty)`

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for
`(-\infty,1)`.

Clearly x=0 belongs to
`(-\infty,1)` interval then plug x=1 into
`(x-1)/(x-3)<0`

`(0-1)/(0-3)<0`

`(-1)/(-3)<0`

`(1)/(3)<0`

Which is False.

Hence
`(-\infty,1)` desn't belongs to the answer.

Similarly testing other intervals, we get that only
`(1,3)` satisfies the original inequality.

Hence final answer is
`(1,3)`.

correct choice is D because both ends are open circles.