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\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}
\frac{1}{\frac{x^b+x^a}{x^b}}+\frac{1}{\frac{x^a+x^b}{x^a}}
\frac{x^a+x^b}{x^a+x^b}
1
Thus, the value of the given equation is 1.
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