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已知分式方程x/(x-1)+k/(x-1)-x/(x+1)=0无解,则实数k的值是
人气:292 ℃ 时间:2019-11-10 08:53:42
解答
(x/x-1)-(k/x-1)-(x/x+1)=0
(x-k)/(x-1)=x/(x+1)
(x-k)(x+1)=x(x-1)
x^2+(1-k)x-k=x^2-x
(2-k)x=k
无解有两种情况
(1)2-k=0
k=2
则(2-k)x=k变成0=2,
不成立,无解
(2)增根,即分母为0
x=k/(2-k)
x+1=0,x-1=0
x=-1,x=1
k/(2-k)=-1,k=k-2,不成立
k/(2-k)=1,k=2-k,k=1
所以k=2或k=1
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