\(\dfrac{x-1}{x+2}+\dfrac{6x}{x^2-4}=\dfrac{x+1}{2-x}\left(dkxd:x\ne\pm2\right)\)
\(\Leftrightarrow\dfrac{x-1}{x+2}+\dfrac{6x}{\left(x-2\right)\left(x+2\right)}=-\dfrac{x+1}{x-2}\)
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x-2\right)+6x+\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow x^2-2x-x+2+6x+x^2+2x+x+2=0\)
\(\Leftrightarrow2x^2+6x+4=0\)
\(\Leftrightarrow2x^2+2x+4x+4=0\)
\(\Leftrightarrow2x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+4=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\left(ktm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)
Vậy \(S=\left\{-1\right\}\)
