1/(x+1)+1/(x+4)=1/(x+2)+1/(x+3)
1/(x+1)--1/(x+3)=1/(x+2)--1/(x+4)
[(x+3)--(x+1)]/(x+1)(x+3)=[(x+4)--(x+2)]/(x+2)(x+4)
2/(x+1)(x+3)=2/(x+2)(x+4)
(x+1)(x+3)=(x+2)(x+4)
x^2+4x+3=x^2+6x+8
2x=--5
x=--2.5
经检验:x=--2.5是原分式方程的解.