(x+3)/(x+2)+(x+7)/(x+6)=(x+4)/(x+3)+(x+6)/(x+5)
1+1/(x+2)+1+1/(x+6)=1+1//(x+3)+1+1/(x+5)
1/(x+2)+1/(x+6)=1/(x+3)+1/(x+5)
(x+6+x+2)/(x+2)(x+6)=(x+5+x+3)/(x+3)(x+5)
(2x+8)/(x+2)(x+6)=(2x+8)/(x+3)(x+5)
∴2x+8=0，或者(x+2)(x+6)=(x+3)(x+5)
解得：x=-4
经检验是原方程的根
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