Question

Prove that 1/1+x^b-a+x^c-a + 1%1+xa-b+x^c-b + 1/1+x^b-c+x^a-c=1​

Answer 1

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Answer 2

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