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用换元法解方程(x-1)/(x+2)-3/(x-1)-1=0
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用换元法解方程(x-1)/(x+2)-3/(x-1)-1=0
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答案和解析
(x-1)/(x+2)-3/(x-1)-1=0
(x-1)/(x+2)-[(x+2)-(x-1)]/(x-1)-1=0
(x-1)/(x+2)-(x+2)/(x-1)+1-1=0
(x-1)/(x+2)-(x+2)/(x-1)=0
设(x-1)/(x+2)=y,则y-1/y=0
即：y²-1=0,解得：y1=1 y2=-1
即：(x-1)/(x+2)=1,或者(x-1)/(x+2)=-1
解得：x=-1/2
经检验是原方程的根
(x-1)/(x+2)-[(x+2)-(x-1)]/(x-1)-1=0
(x-1)/(x+2)-(x+2)/(x-1)+1-1=0
(x-1)/(x+2)-(x+2)/(x-1)=0
设(x-1)/(x+2)=y,则y-1/y=0
即：y²-1=0,解得：y1=1 y2=-1
即：(x-1)/(x+2)=1,或者(x-1)/(x+2)=-1
解得：x=-1/2
经检验是原方程的根
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