Evaluating $\lim_{n\rightarrow \infty} \frac{n\sqrt{\ln n}}{(n+1)\sqrt{\ln(n+1)}}$ I'm supposed to look at
$$\lim_{n\rightarrow \infty} \frac{n\sqrt{\ln n}}{(n+1)\sqrt{\ln(n+1)}}$$
which is of course the result of a ratio test. While Wolfram Alpha tells me the limit is $1$, I don't know how to simplify this expression any further to come to the same conclusion.
Any suggestions on how to proceed would be appreciated. 

$$
\lim_{n \to \infty} \frac{n}{n+1} \cdot \lim_{n \to \infty}\sqrt{\frac{\log n }{\log n + \log(1+\frac{1}{n})}}=1
$$
