1 x( x^2 + 1) = A x + Bx + C ( x^2 + 1) , then (A, ,B, ,C) = - Vidyadip

MCQ

${1 \over {x({x^2} + 1)}} = {A \over x} + {{Bx + C} \over {({x^2} + 1)}}$, then $(A,\,B,\,C) = $

✓
$(1, \,-1,\, 0)$
B
$( - 1,\,0,\, - 1)$
C
$(0,\,1,\,1)$
D
None of these

✓

Answer

Correct option: A.

$(1, \,-1,\, 0)$

a
(a) $A({x^2} + 1) + (Bx + C)x = 1$

For $x = 0,\,A = 1$ and for $x = i$, $ - B + Ci = 1$

$ \Rightarrow B = - 1,\,C = 0$ $ \Rightarrow $ $(A,B,C) = (1,\, - 1,\,0)$.

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