解因式方程：x-4/x-5+x-8/x-9=x-7/x-8+x-5/x-6

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

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

(x-4)/(x-5)+(x-8)/(x-9)=(x-7)/(x-8)+(x-5)/(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)
(2x-14)/[(x-5)(x-9)]=(2x-14)/[(x-8)(x-6)]
当x≠7时,
(x-5)(x-9)=(x-8)(x-6)
-14x+45=-14x+48
45=48
∵45≠48
∴x=7

好强