(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)

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(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)(x-6

(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)
(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)

(x-6)/(x-5)-(x-7)/(x-6)=(x-9)/(x-8)-(x-10)/(x-9)
1-1/(x-5)-1+1/(x-6)=1-1/(x-8)-1+1/(x-9)
1/(x-6)-1/(x-5)=1/(x-9)-1/(x-8)
1/(x-6)+1/(x-8)=1/(x-5)+1/(x-9)
(2x-14)/(x-6)(x-8)=(2x-14)/(x-5)(x-9)
2x-14=0时,等式恒成立,此时x=7
2x-14≠0,x≠7时,(x-6)(x-8)=(x-5)(x-9)
x²-14x+48=x²-14x+45
48=45 不成立
所以x=7
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