Đáp án:
1/4
Giải thích các bước giải:
\(\begin{array}{l}
y = \dfrac{x}{{{{\left( {x + 1} \right)}^2}}} = \dfrac{{x + 1}}{{{{\left( {x + 1} \right)}^2}}} - \dfrac{1}{{{{\left( {x + 1} \right)}^2}}}\left( {x \ne - 1} \right)\\
= - \dfrac{1}{{{{\left( {x + 1} \right)}^2}}} + \dfrac{1}{{x + 1}}\\
= - {\left( {\dfrac{1}{{x + 1}} - \dfrac{1}{2}} \right)^2} + \dfrac{1}{4} \le \dfrac{1}{4}\\
{y_{\max }} = \dfrac{1}{4} \Leftrightarrow \dfrac{1}{{x + 1}} = \dfrac{1}{2} \Rightarrow x = 1\left( {tm} \right)
\end{array}\)
