(a^3+b^3+c^3)/(a^2 *(b+c)+b^2*(a+c)+c^2*(a+b))
=[a^3+(b+c)(b^2+c^2-bc)]/[a^2(b+c)+b^2c+b^2a+c^2a+c^2b]
=[a^3+(b+c)(b^2+c^2-bc)]/[a^2(b+c)+b^2c+a(b^2+c^2)+c^2b]
=[a^3+(b+c)(b^2+c^2-bc)]/[a^2(b+c)+b^2c+a^3+c^2b]
=[a^3+(b+c)(b^2+c^2-bc)]/[a^3+a^2(b+c)+bc(b+c)]
=[a^3+(b+c)(a^2-bc)]/[a^3+(b+c)(a^2+bc)] bc