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If x y z are all different and not equal to zero and  then the value of x-1 + y-1 + z-1 is equal to

  1. -1
  2. - x - y - z
  3.  x-1y-1z-1
  4. xyz

Answer (Detailed Solution Below)

Option 1 : -1
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Detailed Solution

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Calculation:

R1 = R1 - R2

R2 = R2 - R3

Now, Expanding along R1, we get

⇒ x [y(1 + z) - (-z)] - (-y) [0 - (-z)] + 0 = 0

⇒ x [y + yz + z] + y [z] = 0

⇒ xy + xyz + xz + yz = 0

Dividing by xyz

⇒ 

⇒ 

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