`M=(1/a+(a)/(a+1)):(a)/(a^2+a)`
`⇔M=((a+1+a^2)/(a^2+a).(a^2+a)/(a)`
`⇔M=(a^2+a+1)/(a)`
`(a-5)(a+1)=0`
⇔\(\left[ \begin{array}{l}a-5=0\\a+1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}a=5\\a=-1\end{array} \right.\)
với `a=5`
`⇒M=(5^2+5+1)/(5)=(31)/(5)`
`⇔M=(a^2+a+1)/(a)=a+1+1/a≥2\sqrt(a.1/a)+1≥2+1=3`
`"="` xẩy ra khi :
`a=1`