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If a, b, c are all different from zero and `Delta= |[1+a,1,1],[1,1+b,1],[1,1, 1+c]|=0`, then `(1)/(a)+(1)/(b)+(1)/(c)=`

A

`a b c`

B

`(1)/(abc)`

C

`-a-b-c`

D

`-1`

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The correct Answer is:
D
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