Question

(x-4)/(x-5)+(x-8)/(x-9)-(x-5)/(x-6)-(x-7)/(x-8)

Answer 1

(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
(x-4)/(x-5)=[(x-5)+1]/(x-5)=1+1/(x-5),...,所以原方程可化为
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)，
1/(x-5)+1/(x-9)=1/(x-8)+1/(x-6)，
(2x-14)/(x^2-14x+45)=(2x-14)/(x^2-14x+48),
(2x-14)(x^2-14x+48)-(2x-14)(x^2-14x+45)=0,
3(2x-14)=0,
x=7.
经检验，x=7是原方程的解。

Answer 2

(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-5)(x-6)=1/(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7
检验：。。。。。
是原分式方程解
参见
http://zhidao.baidu.com/question/23208861.html