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Please solve for 50 pointsNote :- Don't spam otherwise I will reported your 10 answer ​

Answer»

Hii,

Before you attempt to solve this question, it is worthy to KNOW these formulas :-

\frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ {( {x}^{m}) }^{n} = {x}^{mn}

Now, COMING to the question

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

HENCE PROVED .


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