初二的解方程~

(x-5)/(x-6) + (x-8)/(x-9) = (x-7)/(x-8) + (x-6)/(x-7)
(x-6+1)/(x-6) + (x-9+1)/(x-9) = (x-8+1)/(x-8) + (x-7+1)/(x-7)
1+1/(x-6)+1+1/(x-9) =1+1/(x-8) +1+1/(x-7)
1/(x-6)+1/(x-9) =1/(x-8) +1/(x-7)
(x-9+x-6)/(x-6)(x-9)=(x-7+x-8)/(x-7)(x-8)
(2x-15)*[1/(x-6)(x-9)-1/(x-7)(x-8)]=0
(2x-15)*[1/(x^2-15x+54)-1/(x^2-15x+56)]
因为x^2-15x+54不等于x^2-15x+56
所以2x-15=0
x=15/2
检验，成立

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

(x-5)/(x-6)=[(x-6)+1]/(x-6)=1+1/(x-6),...,所以原方程可化为

1/(x-6)+1/(x-9)=1/(x-8)+1/(x-7)，
(2x-15)/(x^2-15x+54)=(2x-15)/(x^2-15x+56),
(2x-15)(x^2-15x+56)-(2x-15)(x^2-15x+54)=0,
2(2x-15)=0,
x=7. 5
经检验，x=7.5是原方程的解。

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

1+1/(x-6)+1+1/(x-9)=1+1/(x-8)+1+1/(x-7)
即1/(x-6)+1/(x-9)=1/(x-8)+1/(x-7)
通分得
(2x-15)/[(x-6)(x-9)]=(2x-15)/[(x-7)(x-8)]
(1)
当2x-15不等于0时
消去2x-15得到
(x-6)(x-9)=(x-7)(x-8)