`a)`
`x^2+2x+3=(x^2+2x+1)+2`
`=(x+1)^2+2 ge 2 \ \ AAx`
`to 5/(x^2+2x+3) le 5/2`
Dấu "=" xảy ra khi : `(x+1)^2=0`
`<=> x=-1`
Vậy `M_(max)=5/2 <=> x=-1`
`b)`
`4x-5-x^2=-(x^2-4x+5)`
`=-(x^2-4x+4+1)`
`=-[(x-2)^2+1] `
`=-(x-2)^2-1 le -1`
`to 3/(4x-5-x^2) ge 3/(-1)=-3`
Dấu "=" xảy ra khi : `(x-2)^2=0`
`<=> x=2`
Vậy `N_(max)=-3 <=> x=2`