\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For \(A_1 = X\), \(A_2 = X + 1\), \(A_3 = X - 1\) in \(\mathbb{R}[X]\), find \(U_1, U_2, U_3 \in \mathbb{R}[X]\) such that \(A_1 U_1 + A_2 U_2 + A_3 U_3 = 1\).
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