两边乘(m+2n)(m-2n)
(m-2n)(x+1)=2m-(m+2n)(x-1)
(m-2n+m+2n)x=2m+m+2n-m+2n
2mx=2m+4n
有唯一解则x系数不等于0
所以m≠0
且分母不等于0
所以m+2n≠0,m-2n≠0
综上
m≠0且m≠±2n