X+1/X+2+X+6/X+7=X+5/X+6+X+2/X+3 简便方法

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解：原方程化为：1-1/(x+2)+1-1/(x+7)=1-1/(x+6)+1-1/(x+3)1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7)1/[(x+2)(x+3)]=1/[(x+6)(x+7)]即：(x+2)(x+3)=(x+6)(x+7)x²+5x+6=x²+13x+42解得：x=(6-42)/(13-5)=-9/2