(3-x)/(1-x)+(x^2-2)/(x^2-8x+7)=1+(5-x)/(7-x)
(1-x+2)/(1-x)+(x^2-2)/(x^2-8x+7)=1+(5-x)/(7-x)
1+2/(1-x)+(x^2-2)/(x^2-8x+7)=1+(5-x)/(7-x)
2/(1-x)+(x^2-2)/(x^2-8x+7)=(5-x)/(7-x)
2/(1-x)+(x^2-2)/(x^2-8x+7)-(5-x)/(7-x)=0
-2/(x-1)+(x^2-2)/(x^2-8x+7)-(x-5)/(x-7)=0
(x^2-2)/(x^2-8x+7)-2/(x-1)-(x-5)/(x-7)=0
(x^2-2)/(x-7)(x-1)-2(x-7)/(x-7)(x-1)-(x-5)(x-1)/(x-1)(x-7)=0
[(x^2-2)-2(x-7)-(x-5)(x-1)]/(x-1)(x-7)=0
[x^2-2-2x+14-(x^2-6x+5)]/(x-1)(x-7)=0
[x^2-2-2x+14-x^2+6x-5)/(x-1)(x-7)=0
(4x+7)/(x-1)(x-7)=0
4x+7=0
x=-7/4
经检验x=-7/4是方程的解