Đáp án:
$\begin{array}{l}
ap\,dung\,bdt:\left| {a + b} \right| \le \left| a \right| + \left| b \right|\forall a,b\\
\Rightarrow \frac{{\left| {a + b} \right|}}{{2 + \left| {a + b} \right|}} = 1 - \frac{2}{{2 + \left| {a + b} \right|}} \le 1 - \frac{2}{{2 + \left| a \right| + \left| b \right|}} = \frac{{\left| a \right|}}{{2 + \left| a \right| + \left| b \right|}} + \frac{{\left| b \right|}}{{2 + \left| a \right| + \left| b \right|}}\\
\Rightarrow dpcm
\end{array}$
