find limit by rearrangement or L'Hopital's?

Hi, 1st post.

According to my text book the following limit converges to $\displaystyle e^2 $:

$\displaystyle \lim_{n\to\infty}(\frac {n + 3}{n + 1})^n

$

through rearrangement i can achieve this:

$\displaystyle

(\frac {n * (1 + 3/n)} {n * (1 + 1/n)})^n

$

giving...

$\displaystyle

\frac {(1 + 3/n)^n} {(1 + 1/n)^n}

$

The denominator evaluates to $\displaystyle e$ but i can't see how to make the numerator equal to $\displaystyle e^3$ in order to achieve

agreement with the textbook answer. I had a look at using L'Hopital's but

the resulting expression after differentiation looked no simpler.

thanks