Докажите, что верно равенство 1/((a-b)(b-c))-1/((c-a)(c-b))+1/((c-a)(a-b))=0.

\[\frac{1}{(a - b)(b - c)} - \frac{1}{(c - a)(c - b)} + \frac{1}{(c - a)(a - b)} = 0\]

\[\frac{1^{\backslash c - a}}{(a - b)(b - c)} + \frac{1^{\backslash a - b}}{(c - a)(b - c)} + \frac{1^{\backslash b - c}}{(c - a)(a - b)} = 0\]

\[\frac{c - a + a - b + b - c}{(a - b)(b - c)(c - a)} = 0\text{\ \ \ }\]

\[0 = 0\]

\[ч.т.д.\]