Question

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Answer 1

Answer:

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Answer 2

1/(1  + a  + b⁻¹)   + 1/(1 + b  + c⁻¹)   +  1/(1  + c  + a⁻¹) = 1 if abc = 1

Step-by-step explanation:

1/(1  + a  + b⁻¹)   + 1/(1 + b  + c⁻¹)   +  1/(1  + c  + a⁻¹)

= 1/(1  + a  + 1/b)   + 1/(1 + b  + 1/c)   +  1/(1  + c  +1/a)

abc = 1

=> ac = 1/b

or b = 1/ac

= 1/(1  + a  + ac)   + 1/(1 + 1/ac  + 1/c)   +  1/(1  + c  +1/a)

=  1/(1  + a  + ac)  + ac/(ac + 1  + a)   +  a/(a  + ac  + 1)

= 1/(1 + a + ac)  + ac/(1 + a + ac)   + a/(1 + a + ac)

= (1 + ac + a)/(1 + a + ac)

= (1 + a + ac)/(1 + a + ac)

= 1

1/(1  + a  + b⁻¹)   + 1/(1 + b  + c⁻¹)   +  1/(1  + c  + a⁻¹) = 1 if abc = 1

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