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Prove that |(1+a,1, 1),( 1,a+b,1),( 1, 1...

Prove that `|(1+a,1, 1),( 1,a+b,1),( 1, 1, 1+c)|=a b c(a+1/a+1/b+1/c)=a b c+b c+c a+a b`

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Given
`|(1+a,1, 1),( 1,a+b,1),( 1, 1, 1+c)|`
Applying,`R_1​->R_1​−R_2, and ​R_3​->R_3​−R_2`
​`|(a,-b, 0),( 1,1+b,1),( 0, -b, c)|`
=`a(c+bc+b)+bc`
=`ab+bc+ac+abc`
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