So i need to prove that the extension field:

Q(sqrt(2)+sqrt(3)) = the set {a + b.sqrt(2) + c.sqrt(3) + d.sqrt(6) ; with a,b,c,d are rational numbers}

Since Q(sqrt(2)+sqrt(3)) is the SMALLEST field that contains all rationals and sqrt(2)+sqrt(3) hence Q belongs to the set

However, I dont know how to prove the other way around, i.e. the set belongs to Q(sqrt(2)+sqrt(3)).

Can you please help me? Thank you.