Prove that: `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`

Explanation

L.H.S. `= 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/(1 + x^b/x^a + x^c/x^a) + 1/(1 + x^a/x^b + x^c/x^b) + 1/(1 + x^b/x^c + x^a/x^c)`
`= 1/{(x^a+ x^b + x^c)/x^a} + 1/{(x^b + x^a + x^c)/x^b} + 1/{(x^c + x^b + x^a)/x^c}`
`= 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 = `R.H.S.
Hence proved.