用简便方法解方程：1⼀x-5 - 1⼀x-6 = 1⼀x-8 - 1⼀x-9

解：先移相
1/(x-5)-1/(x-8)=1/(x-6）-1/（x-9）
再通分。
3/(x-5)(x-8)=3/(x-6)(x-9)
如此计算便简单多了。
-13x+40=-15x+54
x=7
后面的答案是本人口算的。希望你自己再算一下。

1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
1/(x-5)(x-6)=1/(x-8)(x-9)
(x-5)(x-6)=(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7
经检验,X=7是方程的根

1/x-5 - 1/x-6 = 1/x-8 - 1/x-9
1/x-5+1/x-9=1/x-8+1/x-6
(x-9+x-5)/(x-5)(x-9)=(x-6+x-8)/(x-6)(x-8)
(2x-14)/(x-5)(x-9)=(2x-14)/(x-6)(x-8)
(2x-14)/(x-5)(x-9)-(2x-14)/(x-6)(x-8)=0
2(x-7)[1/(x-5)(x-9)-1/(x-6)(x-8)]=0
2(x-7)[(x-6)(x-8)-(x-5)(x-9)]/[(x-5)(x-9)(x-6)(x-8)]=0
2(x-7)(x^2-14x+48-x^2+14x+45)/[(x-5)(x-9)(x-6)(x-8)]=0
2(x-7)*93/[(x-5)(x-9)(x-6)(x-8)]=0
x=7

http://wenku.baidu.com/view/df65ca284b73f242336c5f1c.html