If \( a, b, c \) are non-zero real numbers, then \( \Delta=\left|\b...

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If \( a, b, c \) are non-zero real numbers, then
\( \Delta=\left|\begin{array}{ccc}1 & a b & \frac{1}{a}+\frac{1}{b} \\ 1 & b c & \frac{1}{b}+\frac{1}{c} \\ 1 & c a & \frac{1}{c}+\frac{1}{a}\end{array}\right| \) is
(a) 0
(b) \( b c+c a+a b \)
(c) \( a^{-1}+b^{-1}+c^{-1} \)
(d) none of these
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