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）

Answer 2

(x-1)/(x-2)+(x-7)/(x-8)=(x-3)/(x-4)+(x-5)/(x-6)
1+1/(x-2)+1+1/(x-8)=1+1/(x-4)+1+1/(x-6)
注释 (x-1)/(x-2)=[(x-2)+1]/(x-2)=(x-2)/(x-2)+1/(x-2)=1+1/(x-2)
1/(x-2)+1/(x-8)=1/(x-4)+1/(x-6)
1/(x-8) -1/(x-6) =1/(x-4)-1(x-2)
[(x-6) -(x-8)]/[(x-6)(x-8)]=[(x-2)-(x-4)]/[(x-4)(x-2)]
2/[(x-6)(x-8)]=2/[(x-4)(x-2)]
(x-6)(x-8)=(x-4)(x-2)
x²-14x+48=x²-6x+8
x=5
检验：

Answer 3

(x-2+1)/(x-2)+(x-8+1)/(x-8)=(x-4+1)/(x-4)+(x-6+1)/(x-6)
1/(x-2)+1/(x-8)=1/(x-4)+1/(x-6)
1/(x-2)-1/(x-4)=1/(x-6)-1/(x-8)
-2/[(x-2)(x-4)]=-2/[(x-6)(x-8)]
(x-2)(x-4)=(x-6)(x-8)
x^2-6x+8=x^2-14x+48
8x=40
x=5

Answer 4

(x-1/x-2)+(x-7/x-8)=(x-3/x-4)+(x-5/x-6)
(x-1/x-2)-(x-5/x-6)=(x-3/x-4)-(x-7/x-8)
[(x-1)(x-6)-(x-5)(x-2)]/[(x-2)(x-6)]=[(x-3)(x-8)-(x-7)(x-4)]/[(x-4)(x-8)]
-4/[(x-2)(x-6)]=-4/[(x-4)(x-8)]
(x-2)(x-6)=(x-4)(x-8)
4x=20
x=5

Answer 5

=5