11 + 2^a - b + 11 + 2^b - a is equal to = ?

Answer: Option C

$$\begin{array}{rl}& \frac{1}{1+2^{a-b}}+\frac{1}{1+2^{b-a}}\\ & =\frac{1}{1+2^{a-b}}+\frac{1}{1+2^{-\left(a-b\right)}}\\ & =\frac{1}{1+2^{a-b}}+\frac{2^{a-b}}{2^{a-b}+1}\\ & =\frac{1+2^{a-b}}{1+2^{a-b}}\\ & =1\end{array}$$