试问当m为何值时,解分式方程1/x-1 + m/x-2 = 2m+2/x^2-3x+2 有增根.
问题描述：
试问当m为何值时,解分式方程1/x-1 + m/x-2 = 2m+2/x^2-3x+2 有增根.
答
1/(x-1)+m/(x-2)=(2m+2)/(x-1)(x-2)
两边乘(x-1)(x-2)
x-2+m(x-1)=2m+2
增根即公分母为0
(x-1)(x-2)=0
x=1,x=2
x=1
代入x-2+m(x-1)=2m+2
-1=2m+2
m=-3/2
x=2
代入x-2+m(x-1)=2m+2
0+m=2m+2
m=-2
所以m=-3/2，m=-2
答
1/(x-1)+m/(x-2)=(2m+2)/(x-1)(x-2)两边乘(x-1)(x-2)x-2+m(x-1)=2m+2增根即公分母为0(x-1)(x-2)=0x=1,x=2x=1代入x-2+m(x-1)=2m+2-1=2m+2m=-3/2x=2代入x-2+m(x-1)=2m+20+m=2m+2m=-2所以m=-3/2,m=-2