Answer:
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
Step-by-step explanation:
Given inequality is [tex]\frac{x-1}{x-3}<0[/tex]
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:
[tex](-\infty,1)[/tex], [tex](1,3)[/tex] and [tex](3,\infty)[/tex]
We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.
Test for [tex](-\infty,1)[/tex].
Clearly x=0 belongs to [tex](-\infty,1)[/tex] interval then plug x=1 into [tex]\frac{x-1}{x-3}<0[/tex]
[tex]\frac{0-1}{0-3}<0[/tex]
[tex]\frac{-1}{-3}<0[/tex]
[tex]\frac{1}{3}<0[/tex]
Which is False.
Hence [tex](-\infty,1)[/tex] desn't belongs to the answer.
Similarly testing other intervals, we get that only [tex](1,3)[/tex] satisfies the original inequality.
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
