Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
A = (\frac{1}{{x - 2}} - \frac{1}{{x + 2}}).\frac{{{x^2} + 4x + 4}}{4}\\
a.ĐK:x \ne \pm 2\\
b.A = \frac{{x + 2 - x + 2}}{{(x - 2).(x + 2)}}.\frac{{{{(x + 2)}^2}}}{4} = \frac{4}{{(x - 2).(x + 2)}}.\frac{{{{(x + 2)}^2}}}{4}\\
= \frac{{x + 2}}{{x - 2}}\\
c.A = \frac{{x - 2 + 4}}{{x - 2}} = 1 + \frac{4}{{x - 2}}
\end{array}\)
A nguyên ⇔\(\frac{4}{{x - 2}}\) nguyên
⇔(x-2) là Ư(4)
\( \Leftrightarrow \left[ \begin{array}{l}
x - 2 = 4\\
x - 2 = - 4\\
x - 2 = 2\\
x - 2 = - 2\\
x - 2 = 1\\
x - 2 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 6(TM)\\
x = - 2(l)\\
x = 4(TM)\\
x = 0(TM)\\
x = 3(TM)\\
x = 1(TM)
\end{array} \right.\)
