For the same u, a₁, a₂, the space Q̄ + Q̄u + Q̄ū + Q̄u/(u² − a₁) + Q̄u/(u² − a₂) contains none of u², ū² and 1/(u − b) with b ∈ Q̄ non-zero

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For the same u, a₁, a₂, the space Q̄ + Q̄u + Q̄ū + Q̄u/(u² − a₁) + Q̄u/(u² − a₂) contains none of u², ū² and 1/(u − b) with b ∈ Q̄ non-zero · Prove2Me