1, $\frac{2mx-1}{x-1}=m-2$ $(x\neq1)$
⇔ $2mx-1=(m-2)(x-1)$
⇔ $2mx-1=x(m-2)-m+2$
⇔ $x.(m+2)=-m+3$
Nếu $m+2=0$ hay $m=-2$ thì $0x=5$
⇒ PT vô nghiệm
Nếu $m+2\neq0$ hay $m\neq-2$ thì $x=\frac{3m}{m+2}$
2, $\frac{2x}{2x²-5x+3}+\frac{9x}{2x²-x-3}=6$
⇔ $\frac{2x}{(3x-2).(x-1)}+\frac{9x}{(3x-2).(x+1)}=6$
⇔ $\frac{2x(x+1)}{(3x-2).(x-1)(x+1)}+\frac{9x(x-1)}{(3x-2).(x+1)(x-1)}=6$
⇒ $2x(x+1)+9x(x-1)=6(3x-2)(x+1)(x-1)$
⇔ $11x²-7x=18x³-12x²-18x+12$
⇔ $18x³-13x²-11x+12=0$