$\frac{a^{3}}{(a+b)(b+c)}+\frac{a+b}{8}+\frac{b+c}{8}\geq \frac{3a}{4}$ (cô-si 3 số)Tương tự:....$\Rightarrow VT+\frac{a+b+c}{2}\geq 3.\frac{a+b+c}{4}$$\Rightarrow$ đpcm
$\frac{a^{3}}{(a+b)(b+c)}+\frac{a+b}{8}+\frac{b+c}{8}\geq \frac{3a}{4}$Tương tự:....$\Rightarrow VT+\frac{a+b+c}{2}\geq 3.\frac{a+b+c}{4}$$\Rightarrow$ đpcm
$\frac{a^{3}}{(a+b)(b+c)}+\frac{a+b}{8}+\frac{b+c}{8}\geq \frac{3a}{4}$
(cô-si 3 số)Tương tự:....$\Rightarrow VT+\frac{a+b+c}{2}\geq 3.\frac{a+b+c}{4}$$\Rightarrow$ đpcm