Question

solve the riddle of maths

Answer 1

$\frac{1}{1 + {x}^{a - b} } + \frac{1}{ {x}^{b - a} } = 1 \\ \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{b} } } + \frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } } = 1 \\ \frac{ {x}^{b} }{ {x}^{a} + {x}^{b} } + \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} } = 1 \\ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} + {x}^{b} } = 1...(proved)$

Answer 2

$\huge{\red{\underline{\textsf{Answer}}}}$

$$\begin{lgathered}\frac{1}{1 + {x}^{a - b} } + \frac{1}{ {x}^{b - a} } = 1 \\ \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{b} } } + \frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } } = 1 \\ \frac{ {x}^{b} }{ {x}^{a} + {x}^{b} } + \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} } = 1 \\ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} + {x}^{b} } = 1...(proved)\end{lgathered}$$

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