The text form of this sum (1/ (1+x^(b-a)+x^(c-a) )+(1/(1+x^(a-b)+x^(c-b) )+(1/(1+x^(b-c)+x^(a-c) )=1 is given below. So that students may not get confused with the text form of the sum.

__Watch video or see this solution__:

First term: (1/ (1+x^(b-a)+x^(c-a) )

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

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

Second term: (1/ (1+x^(a-b)+x^(c-b) )

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

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

Third term: (1/ (1+x^(b-c)+x^(a-c) )

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

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

Therefore

First term+Second term+third term

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

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

=1

LHS=RHS

Proved

Its solution is also given in the video.*keywords:online mathematics, online mathematics degree, online mathematics courses, teaching mathematics.*

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