Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
1.a,ĐK:x \ne \pm 2\\
H = \frac{{{x^2}}}{{x + 2}} - \frac{{{{\left( {x - 2} \right)}^2}}}{2}.\left[ {\frac{{x - 2 + x + 2}}{{{{\left( {x - 2} \right)}^2}\left( {x + 2} \right)}}} \right]\\
= \frac{{{x^2}}}{{x + 2}} - \frac{{{{\left( {x - 2} \right)}^2}}}{2}.\frac{{2x}}{{{{\left( {x - 2} \right)}^2}\left( {x + 2} \right)}}\\
= \frac{{{x^2}}}{{x + 2}} - \frac{x}{{x + 2}} = \frac{{x(x - 1)}}{{x + 2}}
\end{array}\)
b. Để H/x nguyên
\( \Leftrightarrow \frac{{x(x - 1)}}{{x + 2}}.\frac{1}{x} = \frac{{x + 2 - 3}}{{x + 2}} = 1 - \frac{3}{{x + 2}}\) nguyên
⇔x+2 là Ư(3)
\( \Leftrightarrow \left[ \begin{array}{l}
x + 2 = 3\\
x + 2 = - 3\\
x + 2 = 1\\
x + 2 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 1(TM)\\
x = - 5(TM)\\
x = - 1(TM)\\
x = - 3(TM)
\end{array} \right.\)