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

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What is the value of \(\frac{1}{{{x^{\left( {p - q} \right)}} + 1}} + \frac{1}{{{x^{\left( {q - p} \right)}}\; + \;1}}?\)
1). 0
2). 1
3). x(p-q)
4). x(p + q)


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1 answers

2 vote
Answered by on | Votes 2 |

Lets (p – q) = a

Hence, we have

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

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

⇒ [x-a + xa + 2]/[x-a + a + x-a + xa + 1]

⇒ [x-a + xa + 2]/[x-a + xa + 2]

⇒ 1

∴ the correct option is 2)

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