Question

If x, y, z are positive real number and a, b, c are rational numbers, then the value of $\frac{1}{1+x^{b-a}+x^{c-a}}+\frac{1}{1+x^{a-b}+x^{c-b}}+\frac{1}{1+x^{b-c}{x}^{a-c}}$ is

• A. -1
• B. 1
• C. 0
• D. None of these

Answer 1

Answer: (B)

1

Formula used: $x^{a-b}=\frac{x^a}{x^b}$

$\Rightarrow \frac{1}{1+\frac{x^b}{x^a}+\frac{x^c}{x^a}}+\frac{1}{1+\frac{x^a}{x^b}+\frac{x^c}{x^b}}$

$\Rightarrow \frac{x^a}{x^a+x^b+x^c}+\frac{x^b}{x^b+x^a+x^c}+\frac{x^c}{x^c+x^b+x^a}$

$\Rightarrow \frac{x^a+x^b+x^c}{x^a+x^b+x^c}$ ... (Taking LCM)

$\Rightarrow 1$ (Ans)