Question

解因式方程：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)

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