Given an element `alpha` that is transcendental over a field F, which of the following statements about the field extension `F(alpha)"/"F` is correct:
A) The extension field `F(alpha)"/"F` is finite, and every element of `F(alpha)` can be expressed as a polynomial in `alpha` with coefficients from F.
B) The extension field `F(alpha)"/"F` is infinite, and every element of `F(alpha)` can be expressed as a rational function of `alpha` with coefficients from F ?