If the partial fraction decomposition of x 2 + 1 x 3 + 3 x 2 + 3 x + 2 is A x + 2 + B x 2 + x + 1 + C x + 2 x 2 + x + 1 , then A - B + C =

Question

If the partial fraction decomposition of x 2 + 1 x 3 + 3 x 2 + 3 x + 2 is A x + 2 + B x 2 + x + 1 + C x + 2 x 2 + x + 1 , then A - B + C =, 0, 2, 3, 4

MARKS App · Accepted Answer

Given that x 2 + 1 x 3 + 3 x 2 + 3 x + 2 = A x + 2 + B x 2 + x + 1 + C x + 2 x 2 + x + 1 x 2 + 1 = A x 2 + x + 1 + B x + 2 + C .....equation (i) Put x = - 2 5 = A 4 - 2 + 1 + c ⇒ 3 A + C = 5 Comparing coefficients on both the sides of equation (i) we get, A = 1 , A + B = 0 ⇒ B = - 1 C = 5 - 3 A = 2 ∴ A - B + C = 1 + 1 + 2 = 4 .

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