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The value of 1/(1+x^(b-a)+x^(c-a))+1/(1+...

The value of `1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))` is---

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(1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(b-c)+x^(a-c))=1

(1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(a-c)+x^(b-c))

Show that: (1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(b-c)+x^(a-c))=1

Differentiate (1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(a-c)+x^(b-c)) w.r.t. to x.

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))=1