Answer to Question #14487 in Calculus for Joe

Question

I'm in a college pre-calc class and I have a teacher who is notorious for giving incorrect information and the wrong answers to problems. Today he said that ((x^2)-(1/x^2))/((x^2)+(1/x^2) could and should be simplified by multiplying the top and the bottom by x^2 to equal ((x^4)-1)/((x^4)+1). Most of the students said that it was irrational, and didn't follow the rules of mathmatics but he insisted that this was the most simplified form of the problem. Please tell me if he is right or wrong.