.If `a+b+c = 0` then prove that `1/(X^b+X^(-c)+1) +1/(X^c+X^(-a)+1) +1/(X^a+X^(-b)+1) =1`

If a b c = 0, then ({(x^a)^b}^c)/({(x^b)^c}^a) = (a)3 (b) 0 (c) -1 (d) 1

Prove that (x^(b-c))^(a)(x^(a-b))^(c)(x^(c-a))^(b)=1

Prove that: ((x^(a))/(x^(b)))^(c)x((x^(b))/(x^(c)))^(a)x((x^(c))/(x^(a)))^(b)=1

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))=1

-If a,b,c in R then prove that the roots of the equation (1)/(x-a)+(1)/(x-b)+(1)/(x-c)=0 are always real cannot have roots if a=b=c

Prove that :((x^(a))/(x^(b)))^(a+b-c)((x^(b))/(x^(c)))^(b+c-a)((x^(c))/(x^(a)))^(c+a-b)=1