Why is it that when I look at $$\lim\_{x\to\infty} \frac{x}{a+x}$$ 

I don't know the answer because it's an indeterminate form, but if I divide by x 

$$\lim\_{x\to\infty} \frac{1}{\frac{a}{x}+1}$$

the answer appears "magically" ?

What happened ?