Let $x$ be an element of $\mathbb F_q\left(\left(\frac1T\right)\right)$ algebraic over $\mathbb F_q(T)$. Is the extension $\mathbb F_q(T)[x]/\mathbb F_q(T)$ separable? I think it is true but I did not manage to prove it. Thanks in advance
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2$\begingroup$ The answer is yes. This has been asked in a more general setting and answered in mathoverflow.net/questions/287873 $\endgroup$– KConradCommented Sep 6, 2019 at 5:40
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