SOLUTION: Simplify 1/[3^(a-b) + 1] + 1/[3^(b-a) + 1]

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Question 1208088: Simplify
1/[3^(a-b) + 1] + 1/[3^(b-a) + 1]
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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Simplify
1/[3^(a-b) + 1] + 1/[3^(b-a) + 1]
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let  x = 3%5E%28a-b%29,  for brevity.

Then  3%5E%28b-a%29 = 1%2Fx.


So,  1%2F%283%5E%28a-b%29+%2B+1%29 + 1%2F%283%5E%28b-a%29+%2B+1%29 = 1%2F%28x%2B1%29 + 1%2F%28%281%2Fx%29%2B1%29 = 1%2F%28x%2B1%29 + x%2F%28x%2B1%29 = %281%2Bx%29%2F%28x%2B1%29 = 1.    ANSWER

Solved/simplified in one line.