因为：x-5/x-6+x-8/x-9=x-7/x-8+x-6/x-7,所以：1+1/(x-6)+1+1/(x-9)=1+1/(x-8)+1+1/(x-7)
即：1/(x-6）+1/(x-9)=1/(x-8)+1/(x-7)
所以：1/(x-6)-1/(x-7)=1/(x-8)-1/(x-9)
所以：[(x-7)-(x-6)]/[(x-6)(x-7)]=[(x-9)-(x-8)]/[(x-8)(x-9)]
所以：(x-6)(x-7)=(x-8)(x-9)
即：x^2-13x+42=x^2-17x+72,则：4x=30,解得：x=15/2