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If (1)/((1-x)(1-2x)(1-3x))=(A)/((1-x))+(...

If `(1)/((1-x)(1-2x)(1-3x))=(A)/((1-x))+(B)/((1-2x))+(C )/((1-3x))`, then `A+B+C=`________.

A

`0`

B

`1`

C

`-1`

D

`2`

Text Solution

Verified by Experts

`(1)/((1-x)(1-2x)(1-3x))=(A)/(1-x)+(B)/(1-2x)+(C )/(1-3x)`
`=(A(1-2x)(1-3x)+B(1-3x)(1-x)+C(1-x)(1-2x))/((1-x)(1-2x)(1-3x))`
Consider,
`A(1-2x)(1-3x)+B(1-3x)(1-x)+C(1-x)(1-2x)=1`
Comparing constant terms, we get `A+B+C=1`
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