Question

1/(x+1)-1/(x+3)-1/(x+5)+1/(x+7)=0

还有一题
(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)

Answer 1

(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
(x-4)/(x-5)=[(x-5)+1]/(x-5)=1+1/(x-5),...,所以原方程可化为
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)，
1/(x-5)+1/(x-9)=1/(x-8)+1/(x-6)，
(2x-14)/(x^2-14x+45)=(2x-14)/(x^2-14x+48),
(2x-14)(x^2-14x+48)-(2x-14)(x^2-14x+45)=0,
3(2x-14)=0,
x=7.
经检验，x=7是原方程的解。