x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)谁会解这道方程题

x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)谁会解这道方程题
x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)谁会解这道方程题

x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)谁会解这道方程题
x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)
1+2/(x-2)+1-2/(x-7)=1+2/(x-1)+1-2/(x-6)
1/(x-2)-1/(x-7)=1/(x-1)-1/(x-6)
1/(x-2)+1/(x-6)=1/(x-1)+1/(x-7)
(2x-8)/(x^2-8x+12)=(2x-8)/(x^2-8x+7)
由于x^2-8x+12不等于x^2-8x+7
因此,只有2x-8=0
x=4,这个方程只有一个解.

x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)
(x-2+2)/(x-2)+(x-7-2)/(x-7)=(x-1+2)/(x-1)+(x-6-2)/(x-6)
1+2/(x-2)+1-2/(x-7)=1+2/(x-1)+1-2/(x-6)
1/(x-2)-1/(x-7)=1/(x-1)-1/(x-6)
1/(x-2)-1/(x...

全部展开

x/(x-2)+(x-9)/(x-7)=(x+1)/(x-1)+(x-8)/(x-6)
(x-2+2)/(x-2)+(x-7-2)/(x-7)=(x-1+2)/(x-1)+(x-6-2)/(x-6)
1+2/(x-2)+1-2/(x-7)=1+2/(x-1)+1-2/(x-6)
1/(x-2)-1/(x-7)=1/(x-1)-1/(x-6)
1/(x-2)-1/(x-1)=1/(x-7)-1/(x-6)
1/(x-2)(x-1)=1/(x-7)(x-6)
(x-2)(x-1)=(x-7)(x-6)且x不等于1、2、7、6；
则X2-3X+2=X2-13X+42
10X=40
X=4
仅供楼主参考！！！

收起

1+2/(X-2)+1+2/(X-7)=1+2/(X-1)+1+2/(X-6)
1/(X-2)+1/(X-7)=1/(X-1)+1/(X-6)
1/(X-2)-1/(X-1)=1/(X-6)-1/(X-7)
(X-2)(X-1)=(X-6)(X-7)
X^2-3X+2=X^2-13X+42
X=4