若分式方程x+m/x-1-x/x+1=0有增根,则m的值”

Question

若分式方程x+m/x-1-x/x+1=0有增根,则m的值”

Answer 1

x+m/x-1-x/x+1=0
(x+m)(x+1)-x(x-1)=0
x²+(m+1)x+m-x²+x=0
(m+2)x+m=0
有增根,
则,x=±1
当x=1, m=-1
当x = -1 ,m无解,
所以, m = -1