Question
\(\frac{1}{1+x^{(b-a)}+x^{(c-a)}} +\frac{1}{1+x^{(a-b)}+x^{(c-b)}} + \frac{1}{1+x^{(b-c)}+x^{(a-c)}} = ?\)
Answer: Option B
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Given Exp. = \(\frac{1}{\left(1+\frac{x^{b}}{x^{a}}+\frac{x^{c}}{x^{a}}\right)} +\frac{1}{\left(1+\frac{x^{a}}{x^{b}}+\frac{x^{c}}{x^{b}}\right)}+\frac{1}{\left(1+\frac{x^{b}}{x^{c}}+\frac{x^{a}}{x^{c}}\right)}\)
= \(\frac{x^{a}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{b}}{(x^{a}+x^{b}+x^{c})}+\frac{x^{c}}{(x^{a}+x^{b}+x^{c})}\)
= \(\frac{(x^{a}+x^{b}+x^{c})}{(x^{a}+x^{b}+x^{c})}\)
= 1
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