Question

(x-3/x-2)-(x-5/x-4)=(x-7/x-6)-(x-9/x-8)（解方程）

Answer 1

(x-3)/(x-2)-(x-5)/(x-4)=(x-7)/(x-6)-(x-9)/(x-8)
(x-2-1)/(x-2)-(x-4-1)/(x-4)=(x-6-1)/(x-6)-(x-8-1)/(x-8)
1-1/(x-2) -1+1/(x-4) = 1 - 1/(x-6) - 1+ 1/(x-8)
-1/(x-2) + 1/(x-4) = - 1/(x-6)+ 1/(x-8)
1/(x-4)-1/(x-2) = 1/(x-8)-1/(x-6)
(x-2-x+4)/[(x-4)(x-2)] = (x-6-x+8)/[(x-8)(x-6)]
2/[(x-4)(x-2)] = 2/[(x-8)(x-6)]
(x-4)(x-2) = (x-8)(x-6)
x²-6x+8 = x²-14x+48
8x = 40
x = 5，经检验不是增根

追问

(x-2-1)/(x-2)-(x-4-1)/(x-4)=(x-6-1)/(x-6)-(x-8-1)/(x-8)怎么化成1-1/(x-2) -1+1/(x-4) = 1 - 1/(x-6) - 1+ 1/(x-8)

追答

((x-2)-1)/(x-2)-((x-4)-1)/(x-4)=((x-6)-1)/(x-6)-((x-8)-1)/(x-8)
(x-2)/(x-2) - 1/(x-2) - (x-4)/(x-4) +1/(x-4) = (x-6)/(x-6) -1/(x-6) - (x-8)/(x-8) + 1/(x-8)
1-1/(x-2) -1+1/(x-4) = 1 - 1/(x-6) - 1+ 1/(x-8)

Answer 2

(x-3)/(x-2)+(x-9)/(x-8)=(x-5)/(x-4)+(x-7)/(x-6)
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)
(x-8+x-2)/(x²-10x+16)=(x-6+x-4)/(x²-10x+24)
(x-5)(x²-10x+16)=(x-5)(x²-10x+24)
所以只有x=5符合题意
经检验x=5是方程的解

Answer 3

(x-3/x-2)-(x-5/x-4)=(x-7/x-6)-(x-9/x-8)
改写成 (1-1/x-2)-(1-1/x-4)=(1-1/x-6)-(1-1/x-7)，然后把括号去掉，1就消掉了，然后再通分计算，没有好办法，这样运算量会小一些，希望你会看懂我写的式子，按你的写法写的