simplify [(n + 2) / n]^n [(n - 3) / n]^n to find limit

[pamw]

help!

\(\displaystyle \lim_{x \to \infty}
\[
\left( {\frac{{n + 2}}{n}} \right)^n \left( {\frac{{n - 3}}{n}} \right)^n
\]\)

I don't know how to simplify this.

 

[galactus]

Take note that:

\(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=e\)

Therefore, \(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{2}{n}\right)^{n}=e^{2}\)

Can you finish?. See what's going on?.