Field Extensions: Algebraic and Transcendental Elements

Hello there. I have the following problem:

Suppose that is algebraic over for some in an extension field of the field . If is transcendental over , show that is algebraic over .

I've tried writing down the minimal polynomial for over and playing around with that, but I haven't had any luck. I am also somewhat baffled by the transcendental assumption - where does it even come in to play, and how can I write it down? (I usually see it defined as a negative.)

Just a hint in the correct direction would be appreciated.