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

1/1 + x^b a + x^c a + 1/1 + x^a b + x^c b + 1/1 + x^b c + x^a c =x^a/x^a + x^b + x^c + x^b/x^b + x^a + x^c + x^c/x^c + x^b + x^a =x^a+x^b+x^cx^a+ ...

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Integration by Partial Fractions

Prove that : ...

Question

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

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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

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

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

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