I've got this inequality:
And the solutions are supposed to be $(0,1/2)$. But why? Whenever I make my inequality table, it ends up telling me the solution is $(-∞,0) \cup (1/2,+∞)$
Can someone help me understand what is going on? I really need to know this to study for a test.
EDIT: Alright, to make it clearer this is what I've got after simplifying everything:
After that I just put all the values on a table, in which I look for the numbers that make 2x-1 and x equal 0. The polynomial in the numerator can never be zero since its discriminant is less than 0. That's basically where I'm stuck at. I would post the table, but I've no clue where I could create one, I'm doing this on paper.