Question

$\frac{1}{1+x^{(b-a)}+x^{(c-a)}}+\frac{1}{1+x^{(a-b)}+x^{(c-b)}}+\frac{1}{1+x^{(b-c)}+x^{(a-c)}}=?$

• A. $0$
• B. $1$
• C. $x^{a-b-c}$
• D. None of these

Answer 1

The correct option is B $1$

Given Exp. = $\frac{1}{\left(\begin{array}{c}1+\frac{x^b}{x^a}+\frac{x^c}{x^a}\end{array}\right)}+\frac{1}{\left(\begin{array}{c}1+\frac{x^a}{x^b}+\frac{x^c}{x^b}\end{array}\right)}+\frac{1}{\left(\begin{array}{c}1+\frac{x^b}{x^c}+\frac{x^a}{x^c}\end{array}\right)}$
$=\frac{x^a}{(x^a+x^b+x^c)}+\frac{x^b}{(x^a+x^b+x^c)}+\frac{x^c}{(x^a+x^b+x^c)}$
$=\frac{x^a+x^b+x^c}{(x^a+x^b+x^c)}$
$=1.$