1/1+x^a-b+1/1+x^b-a=1
prove that
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The given equation is:
\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}
=\frac{1}{1+\frac{x^a}{x^b}}+\frac{1}{1+\frac{x^b}{x^a}}
=\frac{1}{\frac{x^b+x^a}{x^b}}+\frac{1}{\frac{x^a+x^b}{x^a}}
=\frac{x^b}{x^b+x^a}+\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.
\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}
=\frac{1}{1+\frac{x^a}{x^b}}+\frac{1}{1+\frac{x^b}{x^a}}
=\frac{1}{\frac{x^b+x^a}{x^b}}+\frac{1}{\frac{x^a+x^b}{x^a}}
=\frac{x^b}{x^b+x^a}+\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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