急啊!一道解分式方程!(x-8)/(x-10)+(x-4)/(x-6)=(x-5)/(x-7)+(x-7)/(x-9)

Answer 1

设x-10=A,带入原式
(A+2)/A+(A+6)/(A+4)=(A+5)/(A+3)+(A+3)/(A+1)
1+2/A+1+2/(A+4)=1+2/(A+3)+1+2/(A+1)
1/A+1/(A+4)=1/(A+3)+1/(A+1)
[(A+4)+A]/[A(A+4)]=[(A+1)+(A+3)]/[(A+1)(A+3)]
(2A+4)/[A(A+4)]=(2A+4)/[A(A+4)+3]
1/[A(A+4)]=1/[A(A+4)+3]
3=0
明显不合理,所以,此题无解.