જો ${9 \over {(x - 1)\,{{(x + 2)}^2}}} = {A \over {x - 1}} + {B \over {x + 2}} + {C \over {{{(x + 2)}^2}}}$ તો $A - B - C = $
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c
(c) \(9 = A{(x + 2)^2} + B(x - 1)\,(x + 2)\, + C\,(x - 1)\)
(c) \(9 = A{(x + 2)^2} + B(x - 1)\,(x + 2)\, + C\,(x - 1)\)
For \(x = 1,\,\,9 = 9A \Rightarrow A = 1\)
For \(x = - 2,\,9 = - 3C \Rightarrow C = - 3\)
Equating coefficient of \({x^2},\,0 = A + B \Rightarrow B = - A = - 1\)
\(\therefore A - B - C = 1 - ( - 1) - ( - 3) = 1 + 1 + 3 = 5\).
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