数学问题

在线数学若关于x的方程1/x^2

若关于x的方程1/x^2-1-m/x+1=1-2m/x-1没有产生增根求m 1/(x^2-1)-m/(x+1)=(1-2m)/(x-1) 【等式有意义时，x≠±1】 ===> 1/(x^2-1)-m(x-1)/(x^2-1)=(1-2m)(x+1)/(x^2-1) ===> (1-mx+m)/(x^2-1)=[(1-2m)x+(1-2m)]/(x^2-1) ===> 1-mx+m=(1-2m)x+(1-2m) ===> 1-mx+m-(1-2m)x-(1-2m)=0 ===> 1-mx+m-x+2mx-1+2m=0 ===> (m-1)x+3m=0 ===> (1-m)x=3m 当m≠1时...全部

  若关于x的方程1/x^2-1-m/x+1=1-2m/x-1没有产生增根求m 1/(x^2-1)-m/(x+1)=(1-2m)/(x-1) 【等式有意义时，x≠±1】 ===> 1/(x^2-1)-m(x-1)/(x^2-1)=(1-2m)(x+1)/(x^2-1) ===> (1-mx+m)/(x^2-1)=[(1-2m)x+(1-2m)]/(x^2-1) ===> 1-mx+m=(1-2m)x+(1-2m) ===> 1-mx+m-(1-2m)x-(1-2m)=0 ===> 1-mx+m-x+2mx-1+2m=0 ===> (m-1)x+3m=0 ===> (1-m)x=3m 当m≠1时，x=3m/(1-m) 既然不会产生增根，则：3m/(1-m)≠1，且3m/(1-m)≠-1 所以：m≠-1/2，且m≠1/4。
  收起