Suppose that you have a rational inequality in one variable that you wish to solve. You investigate the inequality and discover the following facts about it:

the left-hand side is always defined;

the right-hand side is undefined when x is 2 but is otherwise defined;

the left-hand side and right-hand side are equal when x is −3/2 and only then;

the original inequality is true when x is −3/2 or 3 but false when x is −2 or 0.

What are the solutions to the inequality?