(2x−m)/(x−2)+(x−1)/(x+2)=3
(2x−m)/(x−2) -1+(x−1)/(x+2)-2=0
{x≠±2)
<=>(4−m)(x+2)−3(x−2)=0
<=>(4−m−3)x+2(4−m)+6=0
<=>(1−m)x=2(m−7)
m=1 vô nghiệm
m khac 1 ⇔x=2(m−7)/(1−m)
nghiệm dương ⇔2(m−7)/(1−m)>0⇔1≤m≤7
⇔(m−7)/(1−m)≠1⇔m≠4
kết luận
[1≤m<4
4<m≤7
\(\dfrac{2x-m}{x-2}+\dfrac{x-1}{x+2}=3\)
\(\Leftrightarrow\dfrac{2x-m}{x-2}-2+\dfrac{x-1}{x+2}-1=0\)
\(\Leftrightarrow\dfrac{4-m}{x-2}+\dfrac{-3}{x+2}=0\\\)
\(\left\{{}\begin{matrix}x\ne\pm2\\\left(4-m\right)\left(x+2\right)-3\left(x-2\right)=0\end{matrix}\right.\)
\(\left(4-m-3\right)x+2\left(4-m\right)+6=0\)
\(\left(1-m\right)x=2\left(m-7\right)\)
m=1 vô nghiệm
m khac 1 \(\Leftrightarrow x=\dfrac{2\left(m-7\right)}{1-m}\)
nghiệm dương \(\Leftrightarrow\dfrac{2\left(m-7\right)}{1-m}>0\Leftrightarrow1\le m\le7\)
\(\Leftrightarrow\dfrac{m-7}{1-m}\ne1\Leftrightarrow m\ne4\)
kết luận
\(\left[{}\begin{matrix}1\le x< 4\\4< x\le7\end{matrix}\right.\)