The discussion revolves around simplifying expressions involving polynomials divided by other polynomials, specifically focusing on the expressions x^2/(1-x) and x^2/(x+2). Participants explore various substitution techniques and algebraic manipulations to approach the problem.
The discussion includes various approaches to simplifying polynomial expressions, with some participants providing algebraic manipulations and others questioning the applicability of certain techniques. There is a recognition of the need for polynomial long division when the degree of the numerator is equal to or greater than that of the denominator.
Participants are navigating the constraints of polynomial degrees and the necessity of polynomial long division in specific cases. There is an emphasis on finding appropriate methods for integration and simplification without reaching a definitive conclusion.
IMO, this is the simplest approach of those presented here.gomunkul51 said:if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).