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If(3x +2 ) /((x + 1 )(2x ^ 2+ 3 )) =(A)/(x + 1 )+ (Bx + C)/(2x ^ 2+3 ),then A + C - Bisequalto

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Solution : ` (3x + 2 ) /((x + 1 )(2x ^ 2+ 3 )) = ( A)/(( x +1 )) + (Bx+ C)/( 2x ^ 2+ 3 )`
` rArr(3x+ 2 )/((x + 1 )(2 x ^ 2+ 3 )) = (A(2x ^ 2+ 3 ) + (x + 1 )(Bx + C))/((x + 1 )(2x ^ 2 + 3 )) `
` rArr3x + 2 = x ^ 2 (2A+ B)+ x (B+ C)+(3A + C) `
` rArr 2A + B = 0 , B + C =3, 3A + C = 2`
`rArrA = (-1)/(5) , B =(2)/(5) , C= (13)/(5) `
`therefore A + C + B =(-1)/(5)+(13)/(5)- (2)/(5) `
` = 2 `


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