x ÷ x-1的差加1等于2x-1除以x 求x

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x ÷ x-1的差加1等于2x-1除以x 求x
x ÷ x-1的差加1等于2x-1除以x 求x

x ÷ x-1的差加1等于2x-1除以x 求x
x/(x-1)+1=(2x-1)/x
[x² +x(x-1)]/x(x-1)=(2x-1)(x-1)/x(x-1)
当x(x-1)≠0
2x²-x=(2x-1)(x-1)
x=x-1无解

[x/(x-1)]+1=(2x-1)/x
x²+x²+x=2x²-3x+1
x=1/4

x / (x-1) + 1 = (2x-1) / x
x / (x-1) = (2x-1) / x - x/x
x / (x-1) = (x-1) / x
x² = (x-1)²
x = ±(x-1)

讨论如下:
(1) 当 x = x - 1 时,
无解。

(2) 当 x = - (x-1) 时,
2x = 1
x = 1/2