SOLUTION: 3. Solve the inequality. Express your solution in interval notation and please be sure to show all of your work. (x-3)²/x(x-1)> 0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3. Solve the inequality. Express your solution in interval notation and please be sure to show all of your work. (x-3)²/x(x-1)> 0      Log On


   

Question 467365: 3. Solve the inequality. Express your solution in interval notation and please be sure to show all of your work.
(x-3)²/x(x-1)> 0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%5E2%2F%28x%28x-1%29%29%3E+0
The critical numbers are 0, 1, 3.
In the interval (-infinity, 0): %28x-3%29%5E2%2F%28x%28x-1%29%29%3E+0. (Use the test number x = -1.)
In the interval (0, 1): %28x-3%29%5E2%2F%28x%28x-1%29%29%3C+0. (Use the test number x = 1/2.)
In the interval (1, 3): %28x-3%29%5E2%2F%28x%28x-1%29%29%3E+0. (Use the test number x = 2.)
In the interval (3,infinity): %28x-3%29%5E2%2F%28x%28x-1%29%29%3E+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).