Prove: \(\frac{1}{1+x^{a-b}} + \frac{1}{1+x^{b-a}} = 1\)

Proof

\[ = \frac{1}{1+x^{a-b}} + \frac{1}{1+x^{-(a-b)}} \]

\[ = \frac{1}{1+x^{a-b}} + \frac{x^{a-b}}{1+x^{a-b}} \]

\[ = \frac{1 + x^{a-b}}{1 + x^{a-b}} \]

\[ = 1 \]

Hence Proved

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