Question

1/1+a^m-n + 1/1+a^n-m​

Answer 1

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To Find :

• The value of 1/1+a^m-n + 1/1+a^n-m

Solution :-

$\frac{1}{1 + {a}^{m - n} } + \frac{1}{1 + {a}^{n - m} } \\ \\ \sf{Taking \: LCM} : \\ \\ = \frac{(1 + {a}^{n - m}) + (1 + {a}^{m - n}) }{ (1 + {a}^{m - n})(1 + {a}^{n - m}) } \\ \\ = \frac{2 +{a}^{n - m} + {a}^{m - n}}{1 + {a}^{m - n} + {a}^{n - m} + {a}^{m - n + n - m} } \\ \\ = \frac{2 +{a}^{n - m} + {a}^{m - n}}{1 + {a}^{m - n} + {a}^{n - m} + {a}^{0} } \\ \\ = \frac{2 +{a}^{n - m} + {a}^{m - n}}{1 + {a}^{m - n} + {a}^{n - m} + 1} \\ \\ = \frac{2 +{a}^{n - m} + {a}^{m - n}}{2 + {a}^{m - n} + {a}^{n - m} } \\ \\ \star \: \underline {\boxed{ = 1}} \: \star$

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