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
6x=42
x=7
经检验x=7是原方程的根