y=lg(x^2+2x)/(x^2+2x+3)
(x^2+2x)/(x^2+2x+3)>0
(x^2+2x)(x^2+2x+3)>0
x(x+2)[(x+1)²+2]>0
(x+1)²+2>0
x<-2或x>0
y=lg(x^2+2x)/(x^2+2x+3)的定义域是x<-2或x>0