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If(1 -x +6 x ^ 2 ) /(x - x ^ 3 )= (A)/(x)+(B)/( 1 - x )+ (C )/(1 +x ) ,then Ais equal to

Answer»

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Solution : ` ( 1- X+6x ^ 2 )/( x (1 -x ^ 2 ) )=(A( 1 -x ^ 2 ) +B(x )(1 + x ) + C(x) (1 - x ))/(x(1 - x )(1 + x)) `
` rArr1- x+6x ^ 2= A (1 - x ^ 2 )+ Bx ( 1 + x ) + Cx( 1 - x ) … (1) `
Substituting`x = 0 `in equation(1)
` I =A(-0 )+ B(0) +C(0) `
` RARR A = 1`


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