40. If $a<-3, m=\frac{a+2}{a+3}, n=\frac{a+1}{a+2}, p=\frac{a}{a+1}$, then the largest among $m, n, p$ is
Answer: $m$.
Solution: Since $\frac{a+2}{a+3}=1-\frac{1}{a+3}, \frac{a+1}{a+2}=1-\frac{1}{a+2}, \frac{a}{a+1}=1-\frac{1}{a+1}$,
and
$$
a+1<a+2<a+3<0,
$$

thus
$$
0<-(a+3)<-(a+2)<-(a+1) \text {. }
$$

Therefore
$$
-\frac{1}{a+1}<-\frac{1}{a+2}<-\frac{1}{a+3} \text {. }
$$

Hence
$$
\frac{a}{a+1}<\frac{a+1}{a+2}<\frac{a+2}{a+3} \text {. }
$$
$m$ is the largest.