Question

Prove That 1/1+x^a-b + 1/1+x^b-a = 1​

Answer 1

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