In a course about Galois theory, there is the following definition :
Let $L_1$ and $L_2$ be two subfields of the field $L$. We define the compositum $L_1L_2$ of $L_1$ and $L_2$ as the smallest subfield of $L$ containing $L_1$ and $L_2$, that is : $$ L_1L_2 = L_2[L_1] = L_1[L_2] $$
So does that mean that $L_1[L_2] = L_1(L_2)$ ? I can't see why.