Question 86

What is the value of $$\frac{1}{x^{(p-q)}+1}+\frac{1}{x^{(q-p)}+1}$$ ?

Solution

Expression : $$\frac{1}{x^{(p-q)}+1}+\frac{1}{x^{(q-p)}+1}$$

= $$\frac{1}{\frac{x^p}{x^q}+1}+\frac{1}{\frac{x^q}{x^p}+1}$$

= $$\frac{1}{\frac{x^p+x^q}{x^q}}+\frac{1}{\frac{x^p+x^q}{x^p}}$$

= $$\frac{x^q}{x^p+x^q}+\frac{x^p}{x^p+x^q}$$

= $$\frac{x^p+x^q}{x^p+x^q}=1$$

=> Ans - (B)

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