x-4/x-6+x-8/x-10=x-5/x-7+x-7/x-9
问题描述：
x-4/x-6+x-8/x-10=x-5/x-7+x-7/x-9
答
(x-8/x-10)-(x-5/x-7)=(x-7/x-9)-(x-4/x-6)
6/(x-10)(x-7)=6/(x-9)(x-6)
(x-10)(x-7)=(x-9)(x-6)
16=2x
x=8
答
2x-12/x-16=2x-12/x-16
x是任意解。
答
(x-10+2)/(x-10)+(x-6+2)/(x-6)=(x-7+2)/(x-7)+(x-9+2)/(x-9)
1+2/(x-10)+1+2/(x-6)=1+2/(x-7)+1+2/(x-9)
1/(x-10)+1/(x-6)=1/(x-7)+1/(x-9)
(x-6+x-10)/(x-10)(x-6)=(x-9+x-7)/(x-7)(x-9)
(2x-16)/(x^2-16x+60)=(2x-16)/(x^2-16x+63)
(2x-16)[1/(x^2-16x+60)-1/(x^2-16x+63)]=0
因为
x^2-16x+60不等于x^2-16x+63
所以1/(x^2-16x+60)-1/(x^2-16x+63)不等于0
所以2x-16=0
x=8
分式方程要检验
经检验,x=8是方程的解