1/(x+1)+1/(x+2)=1/x+1/(x+3)

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1/(x+1)+1/(x+2)=1/x+1/(x+3)
1/(x+1)+1/(x+2)=1/x+1/(x+3)

1/(x+1)+1/(x+2)=1/x+1/(x+3)
1/(x+1)+1/(x+2)=1/x+1/(x+3)
1/(x+2)-1/(x+3)=1/x-1/(x+1)
[(x+3)-(x+2)]/[(x+2)(x+3)]=[(x+1)-x]/[x(x+1)]
1/[(x+2)(x+3)]=1/[x(x+1)]
x(x+1)=(x+2)(x+3)
x^2+x=x^2+5x+6
x-5x=6
-4x=6
x=-1.5
经检验x=-1.5是原方程的解


1/(x+1)+1/(x+2)=1/x+1/(x+3)
1/x-1/(x+1)=1/(x+2)-1/(x+3)
1/[x(x+1)]=1/[(x+2)(x+3)]
x^2+x=x^2+5x+6
4x+6=0
x=-3/2
解毕。