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(x ^ 2+x + 1 ) /((x - 1)(x -2) (x -3))=(A)/(x-1) + (B)/(x-2) + (C )/(x - 3 )rArr A + C =

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Solution : ` ( x ^ 2+ x+ 1 ) /((x - 1 )(x-2) (x - 3 ))= (A)/((x - 1 ))+ (B)/((x - 2 ))+(C )/((x - 3 )) `
`x ^ 2+x + 1=A( x - 2 )(x - 3 ) +B( x - 1 )(x - 3 ) +C( x- 1 )(x - 2 ) `
If`x = 1`
` rArr3=A (-1)( - 2 ) `
` A =(3 ) /(2) `
If`x=3 `
` 3 ^ 2+ 3 + 1=0+0+ C ( 3 - 1 )(3 - 2 ) `
`rArr 13 =2C `
`rArr C =(13 ) /(2) `
A + C `= (3 ) /(2)+ (13 )/(2) `
`thereforeA + C =8 `


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