\(\left\{{}\begin{matrix}\dfrac{3x}{x-1}+\dfrac{2}{y+2}=4\\\dfrac{2x}{x-1}+\dfrac{1}{x+2}=5\end{matrix}\right.\)(ĐKXĐ: \(x\ne1;y\ne-2\))\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3x\left(y+2\right)}{\left(x-1\right)\left(y+2\right)}+\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(y+2\right)}=\dfrac{4\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y+2\right)}\\\dfrac{2x\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}+\dfrac{\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}=\dfrac{5\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3xy+6x+2x-1=4xy+8x-4y-8\\2x^2+4x+x-1=5x^2+10x-5x-10\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4y-xy+7=0\\-3x^2+9=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}4y-xy+7=0\\x=\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4y-\sqrt{3}y+7=0\Leftrightarrow y\left(4-\sqrt{3}\right)y=-7\\x=\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{7}{4-\sqrt{3}}\\x=\sqrt{3}\end{matrix}\right.\)
