sqrt of 3 divided by sqrt of 2 + 2 divided by sqrt of 2

sorry ive been tryin to use latex but i am having difficulty

the answer is sqrt 6 + 2 times sqrt 2 divided by 2

i dont get it, i thought you could add if they have the same deno, and i dont get how they got the numerator, ive checked my book for the lesson that corresponds and it has no example problem

this sucks ive did all the problems leading up to this fine so i dont know where i was supposed to learn problem, i check my algebrator (which sucks ass) and it says something about taking the GCF but i need a human to explain it to me thanks so much