$13 \cdot 32$ The maximum value of the function $y=\frac{3 x^{2}+3 x+4}{x^{2}+x+1}$ is
(A) $4 \frac{1}{3}$.
(B) 4 .
(C) $3 \frac{3}{4}$.
(D) 3 .
(Shandong Province, China Junior High School Mathematics Competition, 1993)
[Solution] From the given, we have $y=3+\frac{1}{x^{2}+x+1}$.
$$
\begin{array}{l}
\because \quad\left(x^{2}+x+1\right)_{\min }=\left(-\frac{1}{2}\right)^{2}+\left(-\frac{1}{2}\right)+1=\frac{3}{4}, \\
\therefore \quad y_{\max }=3+\frac{4}{3}=4 \frac{1}{3} .
\end{array}
$$

Therefore, the correct choice is $(A)$.