2012/018) If 2^x=3^y=6^-z, then find the value of (1/x+1/y+1/z)

we have 2 = 6^(-z/x)
3= 6^(-z/x)

multiply to get 6 = 6^(-z/x-z/y)

or 6^1 = 6^(-z/x-z/y)
or 1= - z/x -z/y

or 1 + z/x + z/y = 0

deviding by z we get 1/z + 1/x + 1/y = 0