(1/x+1)+(1/x+10)=(1/x+2)+(1/x+9)

1

1/(x+1)+1/(x+10)=1/(x+2)+1/(x+9)
(x+1+x+10)/(x+1)(x+10)=(x+2+x+9) /(x+2)(x+9)
(2x+11)/(x+1)(x+10)=(2x+11) /(x+2)(x+9)
(2x+11)/(x+1)(x+10)-(2x+11) /(x+2)(x+9) =0
(2x+11)[1/(x+1)(x+10)-1 /(x+2)(x+9)] =0
(2x+11)[(x+2)(x+9)-(x+1)(x+10)]/(x+1)(x+10)(x+2)(x+9) =0
(2x+11)[x^2+11x+18-(x^2+11x+10)]/(x+1)(x+10)(x+2)(x+9) =0
8(2x+11)/(x+1)(x+10)(x+2)(x+9) =0
8(2x+11)=0
x=-11/2
经检验x=-11/2是方程的解

1/（x+1)+1/（x+10)=1/（x+2)+1/（x+9),1/（x+1)-1/（x+2)=1/（x+9)-1/（x+10)[（x+2）-(x+1)]/(x+!)(x+2)=[(x+10)-(x+9)]/(x+9)(x+10)1/(x+1)(x+2)=1/(x+9)(x+10),(x+1)(x+2)=(x+9)(x+10)x^2+3x+2=x^2+19x+90,16x=-...

1/(x+1)+1/(x+10)=1/(x+2)+1/(x+9)
1/(x+1)-1/(x+2)=1/(x+9)-1/(x+10)
1/((x+1)(x+2))=1/((x+9)(x+10))
(x+1)(x+2)=(x+9)(x+10)
3x+2=19x+90
x=-11/2