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Find constants a and b such that (2x + 17)/(x^2 - x - 2) = a/(x - 2) + b/(x + 1) for all x such that x≠-1 and x≠2.

 Jan 22, 2022
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(2x + 17)/(x^2 - x - 2) = a/(x - 2) + b/(x + 1), (x2 - x - 2) = (x - 2)(x + 1)

(2x + 17) = a(x + 1) + b((x - 2) => (2x + 17) = (a + b)x + (a - 2b)

Equating terms: a + b = 2, a - 2b = 17 => 3b = -15 => b = -5, a = 7

 Jan 22, 2022

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