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(x^(-1)-y^(-1))/(z)+(y^(-1)-z^(-1))/(x)+...

`(x^(-1)-y^(-1))/(z)+(y^(-1)-z^(-1))/(x)+(z^(-1)-x^(-1))/(y)=`_______

A

1

B

-1

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`(x^-1-y^-1)/(z) +(y^(-1)-z^(-1))/(x)+(z^(-1)-x^(-1))/(y)`
`((1)/(x)-(1)/(y))/(z)+((1)/(y)-(1)/(z))/(x)+((1)/(z)-(1)/(x))/(y)`
`(y-x)/(xyz)+(z-y)/(xyz)+(x-z)/(xyz)`
`=(y-x+z-y+x-z)/(xyz)=(0)/(xyz)=0`
Hence, the correct option is (c).
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