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First, perform polynomial division: (x³+1) ÷ (x²+x-2) = x - 1 remainder 3x - 1. So expression = x - 1 + (3x-1)/(x²+x-2). Factor denominator: (x+2)(x-1). Write (3x-1)/[(x+2)(x-1)] = A/(x+2) + B/(x-1). Solve: A = 7/3, B = 2/3. Final: x - 1 + 7/(3(x+2)) + 2/(3(x-1)).
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Zambia