方程m²/(x+2)-(x+5)/(x+2)=1/(x²-4)有增根,求m的值

方程m²/(x+2)-(x+5)/(x+2)=1/(x²-4)有增根,求m的值
方程m²/(x+2)-(x+5)/(x+2)=1/(x²-4)有增根,求m的值

方程m²/(x+2)-(x+5)/(x+2)=1/(x²-4)有增根,求m的值
两边乘(x+2)(x-2)
m²(x+2)-(x+5)(x-2)=1
增根则分母为0
x=2
代入m²(x+2)-(x+5)(x-2)=1
4m²=1
m=±1/2
x=-2
代入m²(x+2)-(x+5)(x-2)=1
1=1
和m无关
所以m=±1/2