解方程(x-1/x-2)+(x-7/x-8)=(x-3/x-4)+(x-5/x-6)谢谢,要过程

Question

解方程(x-1/x-2)+(x-7/x-8)=(x-3/x-4)+(x-5/x-6)
谢谢,要过程

Answer 1

(x-1)/(x-2)+(x-7)/(x-8)=(x-3)/(x-4)+(x-5)/(x-6)
(x-2+1)/(x-2)+(x-8+1)/(x-8)=(x-4+1)/(x-4)+(x-6+1)/(x-6) （此步对分子加1减1,是简便算法）
1+1/(x-2)+1+1/(x-8)=1+1/(x-4)+1+1/(x-6)
1/(x-2)+1/(x-8)=1/(x-4)+1/(x-6)
1/(x-8)-1/(x-4)=1/(x-6)-1/(x-2) （此步移项成左右相减,是再次简便算法）
(x-4-x+8)/(x-8)(x-4)=(x-2-x+6)/(x-6)(x-2)
4/(x-8)(x-4)=4/(x-6)(x-2)
(x-8)(x-4)=(x-6)(x-2)
x^2-12x+32=x^2-8x+12
4x=20
x=5
验算：
1/3-1/3=1-1（验算也正确）