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[latex] \frac{1}{a(b-c)(a-c)} + \frac{1}{b(b-c)(b-a)} + \frac{1}{c(c-a)(c-b)} =\\\\= \frac{1}{a(b-c)(a-c)} +\frac{1}{b(b-c)(b-a)} + \frac{1}{c(a-c)(b-c)}=\\\\= \frac{bc(b-a)+ac(a-c)+ab(b-a)}{abc(b-c)(a-c)(b-a)} = \frac{b^2c-abc+a^2c-ac^2+ab^2-a^2b}{abc(b-c)(a-c)(b-a)} [/latex]