\(ĐK:x\ne\pm2\)
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x+2\right)+5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{-12}{\left(x-2\right)\left(x+2\right)}\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)+5\left(x-2\right)=-12\)
\(\Leftrightarrow x^2+2x-x-2+5x-10=-12\)
\(\Leftrightarrow x^2+6x=0\)
\(\Leftrightarrow x\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=-6\left(tm\right)\end{matrix}\right.\)
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x+2\right)+5\left(x-2\right)+12}{x^2-4}=0\)
\(\Leftrightarrow x^2+2x-x-2+5x-10+12=0\)
\(\Leftrightarrow x^2+6x=0\)
\(\Leftrightarrow x\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-6\end{matrix}\right.\)
