解方程：(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
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(x-4)/(x-5) - (x-5)/(x-6) = (x-7)/(x-8) - (x-8)/(x-9)
(x-5+1)/(x-5) - (x-6+1)/(x-6) = (x-8+1)/(x-8) - (x-9+1)/(x-9)
1+1/(x-5)-1-1/(x-6) = 1+1/(x-8)-1-1/(x-9)
1/(x-5)-1/(x-6) = 1/(x-8)-1/(x-9)
(x-6-x+5)/{(x-5)(x-6)} = (x-9-x+8)/{(x-8)(x-9)
-1/{(x-5)(x-6)} = -1/{(x-8)(x-9)
(x-5)(x-6) = (x-8)(x-9)
x²-11x+30 = x²-17x+72
-11x+17x = 72-30
6x = 42
x = 7
将检验，x=7是原方程的解。
(x-5+1)/(x-5) - (x-6+1)/(x-6) = (x-8+1)/(x-8) - (x-9+1)/(x-9)
1+1/(x-5)-1-1/(x-6) = 1+1/(x-8)-1-1/(x-9)
1/(x-5)-1/(x-6) = 1/(x-8)-1/(x-9)
(x-6-x+5)/{(x-5)(x-6)} = (x-9-x+8)/{(x-8)(x-9)
-1/{(x-5)(x-6)} = -1/{(x-8)(x-9)
(x-5)(x-6) = (x-8)(x-9)
x²-11x+30 = x²-17x+72
-11x+17x = 72-30
6x = 42
x = 7
将检验，x=7是原方程的解。
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