"Let f is a polynomial from k[x,y], where k is a field. Suppose that x appears in f with positive degree. We view f as an element of k(y)[x], that is polynomial in x whose coefficients are rational functions of y." I think I am missing something...why do we need rational functions here? can't we represent any polynomial from k[x,y] as an element of k[y][x] i.e. polynomial in x whose coefficients are polynomials of y?