How do I show that $\frac {a^2}b + \frac {b^2}c + \frac {c^2}a \ge \frac {(a + b + c)(a^2 + b^2 + c^2)}{ab + bc + ca}?$ For positive real numbers $a, b, c$, show that
$$\frac {a^2}b + \frac {b^2}c + \frac {c^2}a \ge \frac {(a + b + c)(a^2 + b^2 + c^2)}{ab + bc + ca}.$$
I don't know how to solve this at all. Can you provide any hints?

$$LHS-RHS=\frac{1}{2(ab+bc+ca)}\cdot \left[\frac{b(ab-c^2)^2}{ca}+\frac{c(bc-a^2)^2}{ab}+\frac{a(ca-b^2)^2}{bc}\right]\ge 0$$
