Given #p+q+r=0#, how do you prove that: #1/(1+x^p+x^(-q))+1/(1+x^q+x^(-r))+1/(1+x^r+x^(-p)) = 1# ?
1 Answer
Mar 25, 2017
See explanation...
Explanation:
Since
#1/(1+x^p+x^(-q))+1/(1+x^q+x^(-r))+1/(1+x^r+x^(-p))#
#=1/(1+x^p+x^(-q))+1/(1+x^q+x^(p+q))+1/(1+x^(-p-q)+x^(-p))#
#=1/(1+x^p+x^(-q))+x^(-q)/(x^(-q)+1+x^p)+x^p/(x^p+x^(-q)+1)#
#=(1+x^p+x^(-q))/(1+x^p+x^(-q))#
#=1#
