Докажите, что верно равенство 1/((х – y)(y – z)) – 1/((y – z)(x – z)) – 1/((z – x)(y – x)) = 0.

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

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

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

\[0 = 0\]

\[ч.т.д.\]