Hi:

If K/F is a finite field extension of degree n, so is K(x)/F(x), where K(x) is the field of rational functions in one variable over K, idem F(x).

I could prove K(x)/F(x) is a finite extension, but I cannot prove the degree is n. It helped me to have found that K(x) = K(p), where p is the polynomial p(x) = x. Analogously, F(x) = F(p). Any hint will be welcome. Thanks for reading.