If ABC=1 , show that 1/1+a+b^-1 + 1/1+b+c^-1 + 1/1+c+a^-1=1

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Solution

1÷(1+a+1/b) here we are dividing and multiplying each term of the denominator by b.now please go throgth the above answer .

abc = 1
ab= 1/c

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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

a b c = 1

\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} + 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

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