How to prove x- a - x- b- 1 - a bx- b - x- c- 1 - b cx- x- a - 1 - c a

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Polynomials

How to prove ...

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How to prove (x^a÷x^b)^1÷ab (x^b÷x^c)^1÷bc (x^c÷x^a)^1÷ca

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{(\frac{x^{a}}{x^{b}})}^{\frac{1}{a b}} . {(\frac{x^{b}}{x^{c}})}^{\frac{1}{b c}} . {(\frac{x^{c}}{x^{a}})}^{\frac{1}{c a}} = 1

(x^a/x^b)^1/ab . (x^b/x^c)^1/bc . (x^c/x^a)^1/ca

∣ ∣ ∣ ∣ ∣ \begin{matrix} u + a^{2} x & w^{'} + a b x & v^{'} + a c x w^{'} + a b x & v + b^{2} x & u^{'} + b c x v^{'} + a c x & u^{'} + b c x & w + c^{2} x \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

\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

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