(x+7)/(x+6)+(x+9)/(x+8)=(x+10)/(x+9)+(x+6)/(x+5)
1+1/(x+6)+1+1/(x+8)=1+1/(1+9)+1+1/(x+5)
1/(x+6)+1/(x+8)=1/(1+9)+1/(x+5)
1/(x+8)-1/(x+9)=1/(x+5)-1/(x+6)
1/(x+8)(x+9)=1/(x+5)(x+6)
(x+8)(x+9)=(X+5)(x+6)
x²+17x+72=x²+11x+30
6x=-42
x=-7
检验：经检验x=-7,是原方程的根
所以原方程的根x=-7