A normalized cubic sum with a pairwise quadratic correction

Let a,b,c>0 Prove that: $\frac {{a^3 + b^3 + c^3 }}{{abc}} + 9\frac {{ab + bc + ac}}{{a^2 + b^2 + c^2 }} \geq 12$ I know it's easy but It is nice. It's must be like this: $\frac {{a^3 + b^3 + c^3 }}{{abc}} + 9\frac {{ab + bc + ac}}{{a^2 + b^2 + c^2 }} \geq 12$ $LHS - RHS = (\sum a^2 - \sum ab)(\sum \frac {1}{ab} - \frac {9}{\sum ab})\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_6962 (Apache-2.0). Complete source proposition preserved; proof developed independently.