Question

$\frac{1}{1 + x {}^{a - b} } + \frac{1}{1 + x {}^{b - a} } = 1$
prove this...
plzz help with proper explanation

Answer 1

Hello Mate

$\frac{1}{1 + {x}^{a - b} } + \frac{1}{1 + {x}^{b - a} } = 1 \\ \frac{1}{1 + \frac{ {x}^{a} }{ {x}^{b} } } + \frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } } = 1 \\ Take LCM of dinominators \\ \frac{ {x}^{b} }{ {x}^{b} + {x}^{a} } + \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} } = 1 \\ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} + {x}^{b} } = 1 \\ 1 = 1$

Hope it helps!