答：4/x+4/(x+5)+(x-4)/(x+5)=1
4/x+(4+x-4)/(x+5)=1
4/x+x/(x+5)=1
4(x+5)/[x(x+5)]+x^2/[x(x+5)]=1
4(x+5)+x^2=x(x+5)
4x+20+x^2=x^2+5x
5x-4x=20
x=20
经检验,x=20是原分式方程的根