x+1/x+2-1/x+7=x+2/x+3-1/x+6
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x+1/x+2-1/x+7=x+2/x+3-1/x+6
x+1/x+2-1/x+7=x+2/x+3-1/x+6
x+1/x+2-1/x+7=x+2/x+3-1/x+6
(x+1)/(x+2)-(x+2)/(x+3)=1/(x+7)-1/(x+6)
[(x+1)(x+3)-(x+2)(x+2)]/(x+2)(x+3)=[x+6-(x+7)]/(x+7)(x+6)
[x^2+4x+3-(x^2+4x+4)]/(x^2+5x+6)=(x+6-x-7)/(x^2+13x+42)
-1/(x^2+5x+6)=-1/(x^2+13x+42)
x^2+5x+6=x^2+13x+42
-8x=36
x=-9/2
括号有点多,不过肯定没错的
(x+1)/(x+2)-(x+2)/(x+3)=1/(x+7)-1/(x+6)
(x+1)(x+3)-(x+2)(x+2)/(x+2)(x+3)=x+6-(x+7)/(x+7)(x+6)
x²+4x+3-(x²+4x+4)/x²+5x+6=x+6-x-7/x²+13x+42
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(x+1)/(x+2)-(x+2)/(x+3)=1/(x+7)-1/(x+6)
(x+1)(x+3)-(x+2)(x+2)/(x+2)(x+3)=x+6-(x+7)/(x+7)(x+6)
x²+4x+3-(x²+4x+4)/x²+5x+6=x+6-x-7/x²+13x+42
-1/x²+5x+6=-1/x²+13x+42
x²+5x+6=x²+13x+42
-8x=36
x=-9/2
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