Evaluate the expression: sum frac{1}{1 + x^{a | vedclass

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(A) Let the expression be $S = \frac{1}{1 + x^{a-b} + x^{a-c}} + \frac{1}{1 + x^{b-a} + x^{b-c}} + \frac{1}{1 + x^{c-a} + x^{c-b}}$.Consider the first

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(A) Let the expression be $S = \frac{1}{1 + x^{a-b} + x^{a-c}} + \frac{1}{1 + x^{b-a} + x^{b-c}} + \frac{1}{1 + x^{c-a} + x^{c-b}}$.Consider the first term: $\frac{1}{1 + \frac{x^a}{x^b} + \frac{x^a}{x^c}} = \frac{x^b x^c}{x^b x^c + x^a x^c + x^a x^b}$.Similarly,the second term becomes $\frac{x^a x^c}{x^b x^c + x^a x^c + x^a x^b}$ and the third term becomes $\frac{x^a x^b}{x^b x^c + x^a x^c + x^a x^b}$.Adding these three terms,we get $\frac{x^b x^c + x^a x^c + x^a x^b}{x^b x^c + x^a x^c + x^a x^b} = 1$.

Evaluate the expression: $\sum \frac{1}{1 + x^{a-b} + x^{a-c}}$

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