lean_workbook_plus_77109

$\sum_{cyc} \frac{a - bc}{a + bc} \leq \frac{3}{2}$\n\n$\Longleftrightarrow \sum{\frac{bc}{a+bc}}\ge \frac{3}{4}$\n\n$\Longleftrightarrow \sum{\frac{bc}{(a+b)(a+c)}}\ge \frac{3}{4}$\n\n$\Longleftrightarrow 4 \sum{bc(b+c)} \ge 3(a+b)(b+c)(c+a)$\n\n$\Longleftrightarrow (a+b)(b+c)(c+a) \ge 8abc$