Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
\frac{{x + 2}}{{x + 1}} + \frac{2}{{y - 2}} = 6\\
\frac{5}{{x + 1}} - \frac{1}{{y - 2}} = 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
1 + \frac{1}{{x + 1}} + \frac{2}{{y - 2}} = 6\\
5.\frac{1}{{x + 1}} - \frac{1}{{y - 2}} = 3
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\frac{1}{{x + 1}} + 2.\frac{1}{{y - 2}} = 5\\
5.\frac{1}{{x + 1}} - \frac{1}{{y - 2}} = 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\frac{1}{{x + 1}} = 1\\
\frac{1}{{y - 2}} = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x + 1 = 1\\
y - 2 = \frac{1}{2}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 0\\
y = \frac{5}{2}
\end{array} \right.
\end{array}$
