\(\left\{{}\begin{matrix}\dfrac{1}{x+1}-\dfrac{3}{y+2}=-2\\\dfrac{2}{x+1}+\dfrac{1}{y+2}=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{x+1}-\dfrac{6}{y+2}=-4\\\dfrac{2}{x+1}+\dfrac{1}{y+2}=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{7}{y+2}=7\\\dfrac{2}{x+1}+\dfrac{1}{y+2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{y+2}=\dfrac{7}{7}=1\\\dfrac{2}{x+1}=3-1=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y+2=1\\x+1=\dfrac{2}{2}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1-2=-1\\x+1=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=0\end{matrix}\right.\)
