Assignment:
Let F be an extension field of K. If u is an element of F is transcendental over K, then show that every element of K(u) that is not in K in also transcendental over K.
Hint for proof: Suppose y is an element of K(u). Then for some g(x), h(x) elements of K[x], we have y = g(u)/h(u). Assume that y is algebraic over K and think about polynomials and u; you can show that y is an element of k.
Provide complete and step by step solution for the question and show calculations and use formulas.