Question

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

Answer 1

(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