解方程(x/x(x+2))+(x/(x+2)(x+4))+.+x/(x+8)(x+10)=1

问题补充：

解方程(x/x(x+2))+(x/(x+2)(x+4))+.+x/(x+8)(x+10)=1

答案：

(x/x(x+2))+(x/(x+2)(x+4))+.+x/(x+8)(x+10)

=(x/2)*(2/x(x+2))+(2/(x+2)(x+4))+.+2/(x+8)(x+10)

=(x/2)*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+.+1/(x+8)-1/(x+10)]

=(x/2)*[1/x-1/(x+10)]

=1/2-x/2(x+10)=1

x/2(x+10)=-1/2

-x=x+10

x=-5分式方程要检验

经检验,x=-5是方程的解

======以下答案可供参考======

供参考答案1:

=x*[(1/x(x+2))+(1/(x+2)(x+4))+......+(1/(x+8)(x+10))]

对方括号内裂项相消得

=x*1/2*(1/x-1/(x+10))=1

故x/(x+10)=-1,x=-5

供参考答案2:

原式=(x/2)*(2/x(x+2))+(2/(x+2)(x+4))+......+2/(x+8)(x+10)

=(x/2)*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+......+1/(x+8)-1/(x+10)]

=(x/2)*[1/x-1/(x+10)]

=1/2-x/2(x+10)=1

x/2(x+10)=-1/2

-x=x+10

x=-5

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