Đáp án:
\(
- \frac{{2(x - 2)}}{{x + 2}}
\)
Giải thích các bước giải:
Ta có:
\(
\begin{array}{l}
\left( {\frac{2}{{x + 2}} - \frac{4}{{x^2 + 4x + 4}}} \right):\left( {\frac{2}{{x^2 - 4}} + \frac{1}{{2 - x}}} \right) \\
= \left( {\frac{{2(x + 2)}}{{(x + 2)^2 }} - \frac{4}{{(x + 2)^2 }}} \right):\left( {\frac{2}{{(x + 2)(x - 2)}} - \frac{{x + 2}}{{(x - 2)(x + 2)}}} \right) \\
= \left( {\frac{{2x + 4 - 4}}{{(x + 2)^2 }}} \right):\left( {\frac{{2 - (x + 2)}}{{(x + 2)(x - 2)}}} \right) \\
= \frac{{2x}}{{(x + 2)^2 }}:\frac{{ - x}}{{(x + 2)(x - 2)}} \\
= \frac{{2x}}{{(x + 2)^2 }}.\frac{{(x + 2)(x - 2)}}{{ - x}} \\
= - \frac{{2(x - 2)}}{{x + 2}} \\
\end{array}
\)
