1.

\left| \begin{array}{ccc}{1+a} & {1} & {1} \\ {1} & {1+b} & {1} \\ {1} & {1} & {1+c}\end{array}\right|=a b c\left(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)

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