\(\Rightarrow m^2x-m^2-4x+6-m=0\) (Chuyển vế, phá ngoặc)
\(\Rightarrow m^2x-4x=m-6+m^2\)
\(\Rightarrow x\left(m^2-4\right)=m-6+m^2\)
\(\Rightarrow x=\frac{m^2+m-6}{\left(m^2-4\right)}=\frac{m^2-2m+3m-6}{\left(m+2\right)\left(m-2\right)}\)(ĐK:\(m\ne\pm2\))
\(\Rightarrow x=\frac{\left(m+3\right)\left(m-2\right)}{\left(m+2\right)\left(m-2\right)}=\frac{m+3}{m+2}\)
Để x nguyên thì \(\left(m+3\right)⋮\left(m+2\right)\)hay\(\left(m+2+1\right)⋮\left(m+2\right)\)
\(\Rightarrow1⋮\left(m+2\right)\Leftrightarrow m+2\in\text{Ư}\left(1\right)=\left\{\pm1\right\}\)
Giải ra đc m = -1 hoặc m = -3
\(\Leftrightarrow m^2x-m^2=4x+m-6\)
\(\Leftrightarrow m^2x-m^2-4x-m+6=0\)
\(\Leftrightarrow x\left(m^2-4\right)-\left(m^2-4\right)-\left(m-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(m^2-4\right)-(m-2)=0\)
\(\Leftrightarrow\left(m-2\right)\left(\left(x-1\right)\left(m+2\right)-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}m=2\left(1\right)\\\left(x-1\right)\left(m+2\right)=1\left(2\right)\end{matrix}\right.\)
Với (1) PT đúng với mọi x
Với (2) \(\Rightarrow x=\frac{1}{m+2}+1\) để x nguyên thì m khác -2, Và \(m+2\inƯ\left(1\right)\Rightarrow m+2=\left(+-1\right)\Rightarrow m=\left(-1,-3\right)\)
(TM m khác +-2)
