$$\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$$     is equal to = ?

A. a - b

B. b - a

C. 1

D. 0

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{ - \left( {a - b} \right)}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{{{2^{a - b}}}}{{{2^{a - b}} + 1}} \cr & = \frac{{1 + {2^{a - b}}}}{{1 + {2^{a - b}}}} \cr & = 1 \cr} $$