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- Hướng dẫn giải

$$\begin{gathered} \lim {\left(2n+1\right)}^2\left(\frac{3}{n^2+2n}-\frac{1}{n^2+3n-1}\right) \\ =\lim \frac{{\left(2n+1\right)}^2\left(2n^2+7n-3\right)}{\left(n^2+2n\right)\left(n^2+3n-1\right)} \\ =\lim \frac{n^2{\left(2+\frac{1}{n}\right)}^2.n^2\left(2+\frac{7}{n}-\frac{3}{n^2}\right)}{n^2\left(1+\frac{2}{n}\right).n^2\left(1+\frac{3}{n}-\frac{1}{n^2}\right)} \\ =\lim \frac{{\left(2+\frac{1}{n}\right)}^2\left(2+\frac{7}{n}-\frac{3}{n^2}\right)}{\left(1+\frac{2}{n}\right)\left(1+\frac{3}{n}-\frac{1}{n^2}\right)}=\frac{2^2.2}{1.1}=8 \end{gathered}$$

Chọn đáp án D