Question

What is it equals to​

Answer 1

1 is the answer

hope it helps

Answer 2

$\mathrm{Question :\;\dfrac{1}{1 + a^{n - m}} + \dfrac{1}{1 + a^{m - n}}}$

$\mathrm{Use\;Law\;of\;Exponents : P^{A + B} = P^A \times P^B}$

$\mathrm{\implies \dfrac{1}{1 + (a^{n})(a^{-m})} + \dfrac{1}{1 + (a^{m})(a^{- n})}}$

$\mathrm{Use\;Law\;of\;Exponents : P^{-A} = \dfrac{1}{P^A}}$

$\mathrm{\implies \dfrac{1}{1 + \dfrac{a^{n}}{a^{m}}} + \dfrac{1}{1 + \dfrac{a^{m}}{a^{n}}}}$

$\mathrm{\implies \dfrac{1}{\dfrac{a^m + a^{n}}{a^{m}}} + \dfrac{1}{\dfrac{a^n + a^{m}}{a^{n}}}}$

$\mathrm{\implies \dfrac{a^m}{a^m + a^{n}} + \dfrac{a^n}{a^n + a^{m}}}$

$\mathrm{\implies \dfrac{a^m + a^n}{a^m + a^{n}}}$

$\mathrm{\implies 1}$