(x-4）/ (x-5) - (x-5)/(x-6) = (x-7) / (x-8) - (x-8) / (x-9)
对方程两边各自通分：
[(x-4)(x-6) - (x-5)(x-5)] / [(x-5)/(x-6)] = [(x-7)(x-9) - (x-8)(x-8)] / [(x-8)(x-9)]
(x^2-10x+24-x^2+10x-25) / [(x-5)/(x-6)] = [x^2-16x+63 - x^2+16x-64] / [(x-8)(x-9)]
1 / [(x-5)/(x-6)] = 1 / [(x-8)(x-9)]
所以：
(x-5)(x-6)=(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7
带入原方程：
左边=-1/2
右边=-1/2
左边=右边
∴x=7是原方程的解
[（x-5)(x-6)]分之1=[（x-8)（x-9)]分之1
(x-5)(x-6)=(x-8)(x-9)
-11x+30=-17x+72
6x=42
x=7
经检验x=7是原方程的解
[1+1/(x-5)]-[1+1/(x-6)]=[1+1/(x-8)]-[1+1/(x-9)]
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
(x-6-x+5)/[(x-5)(x-6)]=(x-9-x+8)/[(x-8)(x-9)]
-1/[(x-5)(x-6)]=-1/[(x-8)(x-9)]
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7
经检验：x=7是原方程的解
1-（x-5分之x-4)+1-(x-6分之x-5）=1-（x-8分之x-7）+1-（x-9分之x-8）
（x-4）/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
{1-1/(x-5)}-{1-1/(x-6)}={1- 1/(x-8)}-{1-1/(x-9)}
1/(x-6)-1/(x-5)=1/(x-9)-1/(x-8)
(x-5-x+6)/(x-5)(x-6)=(x-8-x+9)/(x-8)(x-9)
1/(x-5)(x-6)=1/(x-8)(x-9)
(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
-11x+17x=72-30
6x=42
x=7
解方程 (x-5分之x-4)-(x-6分之x-5)=(x-8分之x-7)-(x-9分之x-8)速度
1 \/ [(x-5)\/(x-6)] = 1 \/ [(x-8)(x-9)]所以：(x-5)(x-6)=(x-8)(x-9)x^2-11x+30=x^2-17x+72 6x=42 x=7 带入原方程：左边=-1\/2 右边=-1\/2 左边=右边 ∴x=7是原方程的解
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