Question

若解关于x的分式方程(x-2)分之2+(x的平方-4)分之mx=(x+2)分之3会产生增根x=2,或x=-2,求m的值

Answer 1

2/(x-2)+mx/(x²-4)=3/(x+2)

2(x+2)/(x-2)(x+2) + mx/(x-2)(x+2)=3(x-2)/(x-2)(x+2)

2(x+2)+mx=3(x-2)

2x+4+mx=3x-6

(1-m)x=10

m=(x-10)/x

x=2时 m=-4

x=-2时 m=6