\(P=\dfrac{3x^2+6x+11}{x^2+2x+3}=\dfrac{3\left(x^2+2x+1\right)+9}{x^2+2x+3}=\dfrac{3.\left(x+1\right)^2+9}{\left(x+1\right)^2+2}=\dfrac{3.\left[\left(x+1\right)^2+2\right]+3}{\left(x+1\right)^2+2}=3+\dfrac{3}{\left(x+1\right)^2+2}\)=> \(P\le3+\dfrac{3}{2}=\dfrac{9}{2}\)

=> \(Max_P=\dfrac{9}{2}\Leftrightarrow x=-1\)

When equality occurs ???

I have got the answer , thanks you all of you :)

thanks 

Cái cậu Lê Anh Tú toàn đi copy bài mấy người khác không ak , người j đâu ấy