[1] \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)}}

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Aptitude

TNPSC G4

10th CBSE Maths

$\dfrac{1}{1+x^{(b-a)}+x^{(c-a)}}+\dfrac{1}{1+x^{(a-b)}+x^{(c-b)}}+\dfrac{1}{1+x^{(b-c)}+x^{(a-c)}}$

x^{a - 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.

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