Докажите, что верно равенство 1/((x-y)(x-z))+1/((y-x)(y-z))+1/((z-x)(z-y))=0.

Ответ:

\[\frac{1}{(a - y)(x - z)} + \frac{1}{(y - x)(y - z)} + \frac{1}{(z - x)(z - y)} = 0\]

\[\frac{1^{\backslash z - y}}{(x - y)(x - z)} + \frac{1^{\backslash x - z}}{(x - y)(z - y)} - \frac{1^{\backslash x - y}}{(x - z)(z - y)} = 0\]

\[\frac{z - y + x - z - x + y}{(x - y)(x - z)(z - y)} = 0\ \ \ \]

\[0 = 0\]

\[ч.т.д.\]