Original sentence: In this setting, a rational expression is a class representative of an equivalence class of formal quotients of polynomials, where P/Q is equivalent to R/S, for polynomials P, Q, R, and S, when PS = QR
Edited sentence: An alternate way of constructing the field of rational expressions over F is by extending the field F by an indeterminant X.Any rational expression can be written as the quotient of two polynomials P/Q with Q ≠ 0, although this representation isn't unique.However since F[X] is a unique factorization domain, there is a unique representation for any rational expression P/Q with P and Q of lowest degree and Q chosen to be monic.In this setting given a field F and some indeterminate X, a rational expression is any element of the field of fractions of the polynomial ring F[X].It can be shown that these two methods are equivalent, and so the field of rational expressions is sometimes denoted F(X) (not to be confused with a function F in some variable X).Like polynomials, rational expressions can also be generalized to n indeterminates X1,..., Xn, by taking the field of fractions of F[X1,..., Xn].P/Q is equivalent to R/S, for polynomials P, Q, R, and S, when PS = QR.This is similar to how a fraction of integers can always be written uniquely in lowest terms by canceling out common factors