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If x , y , z are not all zero such that...

If `x , y , z` are not all zero such that `a x+y+z=0`, `x+b y+z=0`, `x+y+c z=0` then prove that `1/(1-a)+1/(1-b)+1/(1-c)=1`

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`D= | (a,1,1),(1,b,1),(1,1,c)| = 0`
`R_2 -> R_2 - R_1`
`R_3 -> R_3 - cR_1`
`D= |(a,1,1),((1-a),b-1,0,),(1-ac,1-c,0)|`
`=> (1-a)(1-c)- (b-1)(1-ac) = 0`
`= 1-a-c+ac- (b-1-abc+ac) = 0`
`= 1 - a-c+ac-b+1+abc-ac= 0`
`= 2-a-b-c+abc= 0 `
...
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