Let $K$ be a field, and let $A(X)\in K[[X]]$ be a rational formal [power series](/page/Power%20Series). Equivalently, suppose there exist polynomials $P(X),Q(X)\in K[X]$ with $Q(0)\neq 0$ such that
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\begin{align*}
Q(X)A(X)=P(X)
\end{align*}
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in $K[[X]]$. Then $A(X)$ is algebraic over $K(X)$.