lean_workbook_plus_39698

Let $a,b,c,d\geq 0$ ,prove that: \n\n ${\frac {{a}^{3}}{ \left( b+c \right) \left( c+d \right) \left( b+d \right) }}+{\frac {{b}^{3}}{ \left( c+d \right) \left( d+a \right) \left( c+a \right) }}+{\frac {{c}^{3}}{ \left( d+a \right) \left( a+b \right) \left( b+d \right) }}+{\frac {{d}^{3}}{ \left( a+b \right) \left( b+c \right) \left( c+a \right) }}\geq \frac{1}{2}$ \n\n