Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

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

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