若关于x的分式方程x减2分之2x加2减x分之3减m等于3有增根,则m值?

2025-05-04 20:37:38
推荐回答(1个)
回答1:

(2x+2)/(x-2)-(3-m)/x=3
[(2x+2)x-(2x+2)(3-m)]/(x-2)x=3
2x²+2x-6x+2mx-6+2m=3x²-6x
x²-(2+2m)x+6=0
x=[(2+2m)±√(2+2m)²-24]/2=1+m±√m²+2m-5
有增根,x=2 ,或x=0
1+m±√m²+2m-5=2
m-1=±√m²+2m-5
m²-2m+1=m²+2m-5
m=3/2
1+m±√m²+2m-5=0
m²+2m+1=m²+2m-5无解
∴m=3/2