Prove that- 11-xb-a-xc-a-11-xa-b-xc-b-11-xb-c-aa-c-1

L.H.S=11+x^bx^a+x^cx^a+11+x^ax^b+x^cx^b+11+x^bx^c+x^ax^c =x^ax^a+x^b+x^c+x^bx^b+a^a+x^c+x^cx^c+x^b+a^a =x^a+x^b+x^cx^a+x^b+x^c=1=R.H.S ...

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Factorization of a Quadratic Trinomial

Prove that: 1...

Question

Prove that: $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + a^{a - c}} = 1$

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\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1

Prove that:

(i) $\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

(ii) $\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} = 1$

\frac{1}{1 + x^{(b - a)} + x^{(c - a)}} + \frac{1}{1 + x^{(a - b)} + x^{(c - b)}} + \frac{1}{1 + x^{(b - c)} + x^{(a - c)}} = ?

\frac{1}{1 + x^{b - a} + x^{c - a}} + \frac{1}{1 + x^{a - b} + x^{c - b}} + \frac{1}{1 + x^{a - c} + x^{b - c}}

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