\(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\left(đk:x\ne0,x\ne1\right)\)
\(\Leftrightarrow1+\dfrac{2}{x\left(x-1\right)}-\dfrac{2\left(x-1\right)}{x}=0\)
\(\Leftrightarrow\dfrac{x\left(x-1\right)+2-2\left(x-1\right)^2}{x\left(x-1\right)}=0\)
\(\Leftrightarrow x^2-x+2-2x^2+4x-2=0\)
\(\Leftrightarrow-x^2+3x=0\Leftrightarrow x\left(3-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(l\right)\\x=3\left(tm\right)\end{matrix}\right.\)\(\Leftrightarrow x=3\)
\(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{2x-2}{x}=1+\dfrac{2}{x\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{2x-2}{x}-1-\dfrac{2}{x\left(x-1\right)}=0\)
\(\Leftrightarrow\left(2x-2\right)\left(x-1\right)-x\left(x-1\right)-2=0\)
\(\Leftrightarrow2x^2-4x+2-x^2+x-2=0\)
\(\Leftrightarrow x^2-3x=0\)
\(\Leftrightarrow x\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
ĐKXĐ:
x khác 0 và x khác 1
\(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\\< =>\dfrac{2\left(x-1\right)^2}{x\left(x-1\right)}=\dfrac{x\left(x-1\right)}{x\left(x-1\right)}+\dfrac{2}{x\left(x-1\right)}\\ => 2\left(x-1\right)^2=x\left(x-1\right)+2\\ < =>2x^2-4x+2=x^2-x+2\\ < =>x^2-3x=0\\ < =>x\left(x-3\right)=0\\ \)
<=> x =0 (loại) hoặc x= 3
Vậy x=3
\(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\)( \(x\ne0,x\ne1\))
\(\dfrac{2\left(x-1\right)}{x}-\dfrac{2}{x\left(x-1\right)}=1\)
\(\dfrac{2\left(x-1\right)^2-2}{x\left(x-1\right)}=1\)
\(\dfrac{2\left(x^2-2x+1\right)-2}{x\left(x-1\right)}=1\)
\(\dfrac{2\left(x^2-2x+1-1\right)}{x\left(x-1\right)}=1\)
\(\dfrac{2\left(x^2-2x\right)}{x\left(x-1\right)}=1\)
\(\dfrac{2x\left(x-2\right)}{x\left(x-1\right)}=1
\)
\(\dfrac{2\left(x-2\right)}{x-1}=1\)
\(\dfrac{2\left(x-2\right)}{x-1}-1=0\)
\(\dfrac{2x-4-x+1}{x-1}=0\)
\(\dfrac{x-3}{x-1}=0\)
x-3=0
x=3
\(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\)
ĐKXĐ: x \(\ne\) 0; x \(\ne1\)
\(\dfrac{2\left(x-1\right)^2}{x\left(x-1\right)}=\dfrac{x\left(x-1\right)}{x\left(x-1\right)}+\dfrac{2}{x\left(x-1\right)}\)
<=> 2(x - 1)2 = x(x - 1) + 2
<=> 2(x2 - 2x + 1) = x2 - x + 2
<=> 2x2 - 4x + 2 = x2 - x + 2
<=> 2x2 - x2 - 4x + x + 2 - 2 = 0
<=> x2 - 3x = 0
<=> x(x - 3) = 0
<=> \(\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\left(TM\right)\end{matrix}\right.\)
Vậy nghiệm của PT là x = 3
Ta có: \(\dfrac{2\left(x-1\right)}{x}=1+\dfrac{2}{x\left(x-1\right)}\)
\(\Leftrightarrow2\left(x^2-2x+1\right)=x\left(x-1\right)+2\)
\(\Leftrightarrow2x^2-4x+2-x^2+x-2=0\)
\(\Leftrightarrow x\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=3\left(nhận\right)\end{matrix}\right.\)