Question

Prove that :-




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

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Answer 1

This is your answer

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Answer 2

Taking LHS

$\sf \frac{1}{1 + x ^ {a - b}}+ \frac{ 1}{1 + x ^ {b - a}} \\ \\ \sf \: = \frac{ 1}{ 1+ \frac{x^ a }{ x^ b} } + \frac{ 1}{ 1+ \frac{x^ b }{ x^ a} } \\ \\ \sf \: = \frac{1}{ \frac{ {x}^{b} + {x}^{a} }{ {x}^{b} } } + \frac{1}{ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} } } \\ \\ \sf \: = \frac{x^ b}{ x^ b +x^ a} + \frac{ x^ a }{x^ a +x^ b} \\ \\ \sf \: = \frac{ x^ b +x^ a }{x^ a +x^ b} \\ \\ \sf \: =1=RHS \\ \\ \bold \red{ \sf \: Hence \: proved}$

$\red{\underline{ \rule{190pt}{2pt}} }$

$\sf \frac{1 \cancel{00}}{10 \cancel{00}} = \frac{1}{10}$

Used Co`de

\sf \frac{1 \cancel{00}}{10 \cancel{00}} = \frac{1}{10}

Hope it'll help you :-D