Show that a-b-c a -1 b -1 - b -1 c -1 - c -1 a -1 -abc

Multiply Numerator amp; denominator by abc. = (a+b+c)(abc)/(abc)[1a×1b] + (abc)[1b×1c] + (abc)[1c×1a] #160; = (a+b+c)(abc)/(c+a+b) = abc ...

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Rational Expression

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Question

Show that $\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c$

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\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}} = 1

\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + a^{- 1} c^{- 1}} = a b c

a b c = 1

\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}} = 1

if abc=1, show that $\frac{1}{1 + a + b^{- 1}} + \frac{1}{1 + b + c^{- 1}} + \frac{1}{1 + c + a^{- 1}}$ =1

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