please, Im having trouble finding these as x goes to infinity

$\displaystyle sqrt(2x+1)/x+4$ limit is 0 and $\displaystyle sqrt(x^2 + 2x) - x$ limit is 1

for the first I take both sides by 1/x but end up getting $\displaystyle sqrt(2)/1$ and for the second im unsure. i have the answers because of the back of the book but I dont know how to get them