设实数k满足0＜k＜1,解关于x的分式方程x-1分之2k - x²-x分之1 =x分之k+1

题目

设实数k满足0＜k＜1,解关于x的分式方程x-1分之2k - x²-x分之1 =x分之k+1

答案

2k/(x-1)-1/(x²-x)=(k+1)/x
2k/(x-1)-1/[x(x-1)]=(k+1)/x
2kx-1=(k+1)(x-1)
2kx-1=(k+1)x-(k+1)
(2k-k-1)x=1-(k+1)
(k-1)x=-k
x=k/(1-k)