A= \frac{a+b+4}{ab+2a+2b+4} \Leftrightarrow A= \frac{a+b+4}{2(a+b+4) +(ab-4)}Ta có ab \geq 4 \Leftrightarrow ab-4 \geq 0Nên \frac{a+b+4}{2(a+b+4)} \geq \frac{a+b+4}{2(a+b+4)+(ab-4)}\Rightarrow \frac{a+b+4}{2(a+b+4)} \geq \frac{1}{2} \Rightarrow đpcm
$A= \frac{a+b+4}{ab+2a+2b+4} \Leftrightarrow A= \frac{a+b+4}{2(a+b+4) +(ab-4)}
$Ta có
$ab \geq 4 \Leftrightarrow ab-4 \geq 0
$Nên
$\frac{a+b+4}{2(a+b+4)} \geq \frac{a+b+4}{2(a+b+4)+(ab-4)}
$$\Rightarrow \frac{a+b+4}{2(a+b+4)} \geq \frac{1}{2}
$$\Rightarrow đpcm
$