解方程:1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)分析：若直接去分母,运算量很大且复杂,因为本题的构成比较特殊,如果方程两边分别通分,则具有相同的分子,可以使解方程的过程大大简化.仿照此方法,x-4/(x-5)+

Question

解方程:1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
分析：若直接去分母,运算量很大且复杂,因为本题的构成比较特殊,如果方程两边分别通分,则具有相同的分子,可以使解方程的过程大大简化.仿照此方法,
x-4/(x-5)+x-8/(x-9)=x-7/(x-8)+x-5/(x-6)

Answer 1

(x-4)/(x-5)+(x-8)/(x-9)=(x-7)/(x-8)+(x-5)/(x-6)
(x-5+1)/(x-5)+(x-9+1)/(x-9)=(x-8+1)/(x-8)+(x-6+1)/(x-6)
1+1/(x-5)+1+1/(x-9)=1+1/(x-8)+1+1/(x-6)
1/(x-5)+1/(x-9)=1/(x-8)+1/(x-6)
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)
-11x+30=-17x+72
6x=42
x=7
经检验是原方程的根.