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

Question

Question

This question was previously asked in

SSC CGL Previous Paper 14 (Held On: 11 August 2017 Shift 2)

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Answer 1

Lets (p – q) = a

Hence, we have

[1/(x^a + 1)] + [1/(x^-a + 1 )]

⇒ [(x^-a + 1) + (x^a + 1)]/[(x^-a + 1)(x^a + 1)]

⇒ [x^-a + x^a + 2]/[x^{-a + a} + x^-a + x^a + 1]

⇒ [x^-a + x^a + 2]/[x^-a + x^a + 2]

⇒ 1

∴ the correct option is 2)