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Let 2x = 3y = 6-2 = k
= 2x = k
Therefore, k 1/x= 2
Similarly, k 1/y = 3 and k = - 1/z = 6
= k - 1/z=2 × 3
= k - 1/z = k 1/x × k 1/y
= k - 1/z = k 1/x + 1/y
= - 1/2 = 1/x + 1/y
Therefore, 1/x + 1/y + 1/z = 0
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