Simplify-x-y-z-x-1-y-1-z-1-x-1-y-1-z-1-x-y-y-z-z-x-

Question Number 43707 by Tawa1 last updated on 14/Sep/18

Simplify :

(x + y + z) (x^{- 1} + y^{- 1} + z^{- 1}) = (x^{- 1} y^{- 1} z^{- 1}) (x + y) (y + z) (z + x)

Commented by math1967 last updated on 14/Sep/18

S i m p l i f y ? ? ? / p r o v e ? ?

Commented by Tawa1 last updated on 14/Sep/18

It should be prove sir

Commented by Tawa1 last updated on 14/Sep/18

thanks

Answered by math1967 last updated on 14/Sep/18

I t h i n k L . H . S

= (x + y + z) (x^{- 1} + y^{- 1} + z^{- 1}) - 1

= (x + y + z) (\frac{y z + z x + x y}{x y z}) - 1

= \frac{(x + y + z) (x y + y z + z x) - x y z}{x y z}

= \frac{z {(x + y)}^{2} + x y (x + y) + z^{2} (x + y) + x y z - x y z}{x y z}

= \frac{(x + y) (z x + z y + x y + z^{2})}{x y z}

= \frac{(x + y) (y + z) (z + x)}{x y z}

= (\frac{1}{x y z}) (x + y) (y + z) (z + x)

= (x^{- 1} y^{- 1} z^{- 1}) (x + y) (y + z) (z + x)

= R . H . S

Commented by Tawa1 last updated on 14/Sep/18

God bless you sir

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