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6. If \( a b c=1 \), show that \( \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1 \)

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6. If \( a b c=1 \), show that \( \frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1 \)
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Let Z \(=\frac {1}{1+a + b^{-1}} + \frac {1}{1+b + c^{-1}} + \frac {1}{1+c +a ^{-1}}\)

If abc = 1 then

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