2x^2-4x-3/x^2-2x-1=3解分式方程

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2x^2-4x-3/x^2-2x-1=3解分式方程

2x^2-4x-3/x^2-2x-1=3解分式方程
2x^2-4x-3/x^2-2x-1=3解分式方程

2x^2-4x-3/x^2-2x-1=3解分式方程
第三项的分母是x^2-2x-1吧?
2x^2-4x-3/(x^2-2x-1)=3
2x^2-4x-3-3/(x^2-2x-1)=0
2(x^2-2x-1)-1-3/(x^2-2x-1)=0
2(x^2-2x-1)^2-(x^2-2x-1)-3=0
令a=x^2-2x-1
原方程转化为2a^2-a-3=0
(2a-3)(a+1)=0
a1=3/2,a2= -1
于是可得到两个方程:
x^2-2x-1= -1 (1)
x^2-2x-1= 3/2 (2)
由(1)得:x^2-2x=0
x1=2,x2=0
由(2)得:2x^2-4x-5=0
x3=(2+根号14)/2,x4=(2-根号14)/2
因此原方程的解是x1=2,x2=0,x3=(2+根号14)/2,x4=(2-根号14)/2

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2x^2-4x-3/x^2-2x-1=3
2x^2-4x-3/x^2-2x-1=3x^2-6x-3/x^2-2x-1
2x^2-4x-3=3x^2-6x-3
x^2-2x=0
x=0或者x=2
带入x^2-2x-1计算
当x=2或x=0时
x^2-2x-1≠0
所以x=2或x=0

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