$\dfrac{1}{1+x^{(b-a)}+x^{(c-a)}}+\dfrac{1}{1+x^{(a-b)}+x^{(c-b)}}+\dfrac{1}{1+x^{(b-c)}+x^{(a-c)}}$
0
1
xa - b - c
None of these
Explanation:
Given Exp. = $\dfrac{1}{\left(1+\dfrac{x^{b}}{x^{a}}+\dfrac{x^{c}}{x^{a}}\right)} + \dfrac{1}{\left(1+\dfrac{x^{a}}{x^{b}}+\dfrac{x^{c}}{x^{b}}\right)}+\dfrac{1}{\left(1+\dfrac{x^{b}}{x^{c}}+\dfrac{x^{a}}{x^{c}}\right)}$
=$ \dfrac{x^{a}}{x^{a}+x^{b}+x^{c}}+\dfrac{x^{b}}{x^{a}+x^{b}+x^{c}}+\dfrac{x^{c}}{x^{a}+x^{b}+x^{c}}$
=$\dfrac{x^{a}+x^{b}+x^{c}}{x^{a}+x^{b}+x^{c}}$
= 1.
Given Exp. = $\dfrac{1}{\left(1+\dfrac{x^{b}}{x^{a}}+\dfrac{x^{c}}{x^{a}}\right)} + \dfrac{1}{\left(1+\dfrac{x^{a}}{x^{b}}+\dfrac{x^{c}}{x^{b}}\right)}+\dfrac{1}{\left(1+\dfrac{x^{b}}{x^{c}}+\dfrac{x^{a}}{x^{c}}\right)}$
=$ \dfrac{x^{a}}{x^{a}+x^{b}+x^{c}}+\dfrac{x^{b}}{x^{a}+x^{b}+x^{c}}+\dfrac{x^{c}}{x^{a}+x^{b}+x^{c}}$
=$\dfrac{x^{a}+x^{b}+x^{c}}{x^{a}+x^{b}+x^{c}}$
= 1.