\(\dfrac{x+2}{x-2}-\dfrac{2}{x^2-2x}=\dfrac{1}{x}\)
\(\Leftrightarrow\dfrac{x+2}{x-2}-\dfrac{2}{x\left(x-2\right)}=\dfrac{1}{x}\)
ĐKXĐ:\(\left\{{}\begin{matrix}x\ne0\\x\ne2\end{matrix}\right.\)
\(\Leftrightarrow\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{2}{x\left(x-2\right)}=\dfrac{x-2}{x\left(x-2\right)}\)
\(\Leftrightarrow x^2+2x-2=x-2\)
\(\Leftrightarrow x^2+x=0\Leftrightarrow x\left(x+1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\left(kTM\right)\\x=-1\left(TM\right)\end{matrix}\right.\)
Vậy phương trình đã cho có nghiệm \(x=-1\)
Ta có: \(\dfrac{x+2}{x-2}-\dfrac{2}{x^2-2x}=\dfrac{1}{x}\)
\(\Leftrightarrow x\left(x+2\right)-2=x-2\)
\(\Leftrightarrow x^2+2x-x=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
hay x=-1
