\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\) \(\left(x\ne0,2\right)\)
\(\Leftrightarrow\frac{x\left(x+2\right)-x+2}{x\left(x-2\right)}=\frac{2}{x\left(x-2\right)}\)
\(\Rightarrow x^2+2x-x+2-2=0\)
\(\Leftrightarrow x^2+x=0\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loai\right)\\x=-1\left(t/m\right)\end{matrix}\right.\)
\(\frac{2x}{2x-1}+\frac{x}{2x+1}=1+\frac{4}{\left(2x-1\right)\left(2x+1\right)}\left(x\ne\overset{+}{-}\frac{1}{2}\right)\)
\(\Leftrightarrow\frac{2x\left(2x+1\right)+x\left(2x-1\right)}{\left(2x+1\right)\left(2x-1\right)}=\frac{4x^2-1+4}{\left(2x-1\right)\left(2x+1\right)}\)
\(\Rightarrow4x^2+2x+2x^2-x-4x^2-3=0\)
\(\Leftrightarrow2x^2+x-3=0\)
\(\Leftrightarrow2x^2+3x-2x-3=0\)
\(\Leftrightarrow\left(2x+3\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-\frac{3}{2}\\x=1\end{matrix}\right.\)
\(\frac{2x-1}{3}+x=\frac{x+4}{2}\)
\(\Leftrightarrow\frac{2x-1+3x}{3}=\frac{x+4}{2}\)
\(\Leftrightarrow2\left(5x-1\right)-3\left(x+4\right)=0\)
\(\Leftrightarrow10x-2-3x-12=0\)
\(\Leftrightarrow7x-14=0\Leftrightarrow x=2\)
\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x^2-2x}\)
\(\Rightarrow\frac{x\left(x+2\right)}{x\left(x-2\right)}-\frac{1\left(x-2\right)}{x\left(x-2\right)}=\frac{2}{x\left(x-2\right)}\)
\(\Rightarrow x\left(x+2\right)-1\left(x-2\right)=2\)
\(\Rightarrow x^2+2x-x+2=2\)
\(\Rightarrow x^2+x=2-2\)
\(\Rightarrow x\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
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