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Field Extension/Transcendental

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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.

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This solution is comprised of a detailed explanation to show that every element of K(u) that is not in K in also transcendental over K.

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Problem: 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.

Proof:
Suppose y is an element of K(u), then ...

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