该题假设是n正数.
(n^2+6n+8)/(n^2+3n)=((n+2)*(n+4))/(n*(n+3)),考察该式随n的增大时的情况,
由n^2+3n+2>n^2+3n,(n+1)*(n+2)>n*(n+3),得(n+2)/n>(n+3)/(n+1)
由n^2+8n+16>n^2+8n+15,(n+4)*(n+4)>(n+3)*(n+5),得((n+4)/(n+3)>(n+5)/(n+4),于是得
((n+2)*(n+4))/(n*(n+3))>((n+3)*(n+5))/((n+1)*(n+4))
即当n增大该式的值也减小,故该式没有最小值,当n=1取得最大值15/4.