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)
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)