用换元法解方程2x÷x-1

原方程等价于2x+8/x-5=0因为x不为零,可以两边同时乘以x,得到2x²-5x+8=0这个方程无解所以原方程无解原方程无解是肯定无疑的,如果楼主学过均值不等式或者导数,就可以知道：f(x

令t=x/(x²-1)；则有：3t+1/(2t)=5/2;6t²+1-5t=0;(2t-1)(3t-1)=0;t=1/2或t=1/3;∴x/x²-1=1/2;x²

设3x^+2x+1=a则a-2=3/a解得a=3或-1∴3x^+2x+1=3或-1当3x^+2x+1=3得x=(-1±√7)/3当3x^+2x+1=-1得无解∴x=(-1±√7)/3

设3x/（x^2-1）=t,则t+1/t=5/2,去分母得t^2-5t/2+1=0,即(t-2)(t-1/2)=0,所以t=2或t=1/2,当t=2时得3x/（x^2-1）=2,即2x^2-3x-2=

X^2+1/x^2-2（x+1/x）-1=0(X+1/X)^2-2(X+1/X)-3=0x+1/x=YY^2-2Y-3=0(Y-3)(Y+1)=01)Y=3X+1/X-3=0X^2-3X+1=0X=（

令(x+1)/x^2=y则x^2/(x+1)=1/y原方程可化为y-2/y=1即y^2-y-2=0(y-2)(y+1)=0y=2或y=-1当y=2即(x+1)/x^2=2则2x^2-x-1=0(2x+

设3x平方/x+1=T则方程为T-(3/T)=2同分母得T平方-2T-3=0所以T=-1或3若T=3则3x平方/x+1为3这种有分数的方程要同分母才能求值x=.（好像有根号）若T=-1则3x平方/x+

设x2+2x=y，则原方程为y-6y=1．解之得，y1=3，y2=-2．则x2+2x=3或x2+2x=-2，当x2+2x＝3时，有x2-3x+2=0，解之得，x1=1，x2=2．当x2+2x＝−2时，

令a=x²+x则3a=2/a+13a²-a-2=0(3a+1)(a-1)=0a=-1/3,a=1x²+x=-1/33x²+3x+1=0无解x²+x=1

设y=x2+x，则得y+1=2y，方程两边同乘以y，整理得y2+y-2=0．故本题答案为：y2+y-2=0．

[x/(x-1)]^2-2[x/(1-x)]-3=0[x/(x-1)]^2+2[x/(x-1)]-3=0设t=x/(x-1),则x=t/(t-1)t^2+2t-3=0(t-1)(t+3)=0tS

（2x÷x²-1）-1÷x²-x=0（2/x-1）-1/x²-x=02/x-1-1/x²-x=0x+1-2/x+1/x²=0x³+x

x/(x-2)=2x/(x-3)+(1-x)/(x-5x+6)x/(x-2)=2x/(x-3)+(1-x)/(x-2)(x-3)x(x-3)/(x-2)(x-3)=2x(x-2)/(x-2)(x-3)

由2x−1x=y可得x2x−1＝1y．所以原方程可化为y-1y=2，整理得y2-2y-1=0．

令x-2/x=t,则t^2-2t+1=0,t=1,所以x-2/x=1,即x^2-x-2=0,解得x=2,或x=-1

设x−1x+3＝y，那么x+3x−1＝1y，原方程变形为2y+6y＝7，整理得2y2-7y+6=0．解这个方程，得y1＝32，y2=2．当y＝32时，x−1x+3＝32，去分母，得3x+9=2x-2，

设x-2/x=t则t-3/t=2t^2-3=2tt^2-2t-3=0(t-3)(t+1)=0t=3或-1若t=3x-2/x=3,x=-1若t=-1x-2/x=-1,x=1经检验,x1=-1x2=1均为

设y=x²+2x,则原方程可变为：y-6/y=1y²-6=yy²-y-6=0(y+2)(y-3)=0y=-2y=3所以x²+2x=-2解这个方程无解x²

令a=x²-1则x²-2=a-1所以a-1=2/a两边乘aa²-a-2=0(a+1)(a-2)=0a=-1,a=2x²-1=-1x²=0x=0x

=[3/(x+1)-(x-1)]÷(x²-2x)/(x+1)=[3/(x+1)-(x-1)(x+1)/(x+1)]÷x(x-2)/(x+1)=[3-(x+1)(x-1)]/(x+1)÷x(x