Question 168
Prove that for all $a, b, c \gt 0$ we have
$$
\frac{a^{2}}{b^{3} c} - \frac{a}{b^{2}} \geq \frac{c}{b} - \frac{c^{2}}{a} .
$$
In which case does equality hold?
$$
\frac{a^{2}}{b^{3} c} - \frac{a}{b^{2}} \geq \frac{c}{b} - \frac{c^{2}}{a} .
$$
In which case does equality hold?