Question

Simplify $\frac{1}{1+a^{m-n}}+\frac{1}{1+a^{n-m}}$

Answer 1

We have,

$\frac{1}{1+a^{m-n}}+\frac{1}{1+a^{n-m}}$

$=\frac{1}{1+\frac{a^m}{a^n}}+\frac{1}{1+\frac{a^n}{a^m}}$

$=\frac{a^n}{a^m+a^n}+\frac{a^m}{a^m+a^m}$

$=\frac{a^n+a^m}{a^m+a^n}=1$

Hence, this is the answer.