limits of the sequence $n/(n+1)$ Given the problem:
Determine the limits of the sequnce $\{x_n\}^
\infty_{
n=1}$
$$x_n = \frac{n}{n+1}$$
The solution to this is:  
step1:  
$\lim\limits_{n \rightarrow \infty} x_n = \lim\limits_{n \rightarrow \infty} \frac{n}{n + 1}$  
step2:  
$=\lim\limits_{n \rightarrow \infty} \frac{1}{1+\frac{1}{n}}$  
step3:  
$=\frac{1}{1 + \lim\limits_{n \rightarrow \infty} \frac{1}{n}}$  
step4:  
$=\frac{1}{1 + 0}$  
step5:  
$=1$
I get how you go from step 2 to 5 but I don't understand how you go from step 1 to 2.
Again, I'm stuck on the basic highschool math.
Please help

Divide the numerator and denominator by $n$. Why is this legal, in other words, why does this leave your fraction unchanged? 

Because $$\frac {\frac a n} {\frac b n}=\frac {a \cdot \frac 1 n} {b \cdot \frac 1 n}=\frac a b$$ where the last equality is because $\dfrac 1 n$'s get cancelled. 

Further, remember the fact that: 
$$\frac{a+b}{n}=\frac a n+\frac b n$$
