Split P(x)/((x−r₁)(x−r₂)…) into simple fractions via cover-up.
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Answer
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Why it works
Heaviside’s cover-up: multiply both sides by (x−rᵢ) and set x = rᵢ — every other term vanishes, leaving Aᵢ = P(rᵢ)/∏(rᵢ−rⱼ) directly. It is the reverse of adding fractions, and the key that makes rational integrals doable.
