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

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

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

解方程:(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(x-9)
(x-4)/(x-5)-(x-5)/(x-6)=(x-7)/(x-8)-(x-8)/(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)
通分:
-1/[(x-5)(x-6)]=-1/[(x-8)(x-9)]
(x-5)(x-6)=(x-8)(x-9)
x^2-11x+30=x^2-17x+72
6x=42
x=7

=>
1/(x-5) - 1/(x-6) = 1/(x-8) - 1/(x-9)
=>
1/(x-5) + 1/(x-9) = 1/(x-6) + 1/(x-8)
=>
(2x-14)/(x-5)(x-9) = (2x-14)/(x-6)(x-8)
=>
x = 7

(x-5)(x-9) = (x-6)(x-8)
=>无解
所以
x=7