Let $R(t_1, \cdots, t_n)\in \mathbb{R}(t_1, \cdots, t_n)$ be a rational function in $n$ variables. Suppose $R_i:=R(1, 1, \cdots, 1, t_i, 1, 1, \cdots, 1)$ is a polynomial in $t_i$ for $1\leq i\leq n$. Is it true that $R(t_1, \cdots, t_n)$ is a polynomial?
2026-03-30 04:43:44.1774845824
Rational function and polynomials
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$R(x, y) = \frac{xy + 1}{x + y}$