# 1/x + 1/y + 1/z is equal to

If 2^{x} = 3^{y} = 6^{-z} then 1/x + 1/y + 1/z is equal to

(a) 3/2

(b) 1

(c) 0

(d) -1/2

**Answer: (c) 0 **

**Solution:-**

Let 2^{x} = 3^{y} = 6^{-z} = k

2^{x} = k

Therefore, k^1/x = = 2

Similarly, k^1/y= 3 and k^-1/z = 6

=> k^-1/z = 2 x 3

= k^-1/z = k^1/x + k^1/y

= k^-1/z = k^(1/x + 1/y)

Comparing on both side,

-1/z = 1/x + 1/y

Therefore,

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

Hence, the correct answer is option (c) 0.