方程：1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)=4/21的解是

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方程：1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)=4/21的解是
方程：1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)=4/21的解是

方程：1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)=4/21的解是
图片回答

1/(x^2+x)+1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)=4/21
1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+1/[(x+3)(x+4)]=4/21
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=4/21
1/x-1/(x+4)=4/21
4/[x(x+4)]=4/21
x(x+4)=21
x=-7或x=4
经检验，两个解都满足原方程，故x=-7或x=4

1 1 1 1 4
-------- +------------ + ------------ + --------------- =---------
x^2+x x^2+3x+2 x^2+5x+6 ...

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1 1 1 1 4
-------- +------------ + ------------ + --------------- =---------
x^2+x x^2+3x+2 x^2+5x+6 x^2+7x+12 21
1 1 1 1 4
--------- +---------------- +---------------- +-------------- =-------
x(x+1) (x+1)(x+2) (x+2)(x+3) (x+3)(x+4) 21
1 1 1 1 1 1 1 1 4
--- -- ------ +-------- - ------- + ------- - ---------- + ---------- - --------- = -----------
x x+1 x+1 x+2 x+2 x+3 x+3 x+4 21
1 1 4
---- - ------- = --------
x x+4 21
x(x+4)=21
x=3、-7

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