Question 467365
{{{(x-3)^2/(x(x-1))> 0}}}

The critical numbers are 0, 1, 3.

In the interval ({{{-infinity}}}, 0): {{{(x-3)^2/(x(x-1))> 0}}}. (Use the test number x = -1.)

In the interval (0, 1): {{{(x-3)^2/(x(x-1))< 0}}}. (Use the test number x = 1/2.)

In the interval (1, 3): {{{(x-3)^2/(x(x-1))> 0}}}. (Use the test number x = 2.)

In the interval (3,{{{infinity}}}): {{{(x-3)^2/(x(x-1))> 0}}}. (Use the test number x = 4.)
The critical numbers are not included in the solution set.  (Why?)

Hence the solution set is  ({{{-infinity}}}, 0)U(1, 3)U (3,{{{infinity}}}).