1/1+x^a-b+1/1+x^b-a = 1
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The given equation is:
\frac{1}{1+x^{a-b}}+\frac{1}{1+x^{b-a}}
1+x
a−b
1
+
1+x
b−a
1
=\frac{1}{1+\frac{x^a}{x^b}}+\frac{1}{1+\frac{x^b}{x^a}}
1+
x
b
x
a
1
+
1+
x
a
x
b
1
=\frac{1}{\frac{x^b+x^a}{x^b}}+\frac{1}{\frac{x^a+x^b}{x^a}}
x
b
x
b
+x
a
1
+
x
a
x
a
+x
b
1
=\frac{x^b}{x^b+x^a}+\frac{x^a}{x^b+x^a}
x
b
+x
a
x
b
+
x
b
+x
a
x
a
=\frac{x^a+x^b}{x^a+x^b}
x
a
+x
b
x
a
+x
b
=11
Thus, the value of the given equation is 1.
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