Proof that recursive languages are closed under concatenation
Imagine you have an algorithm $A$ that decides $L_A$ and an algorithm $B$ that accpts $L_B$. How would you write a program that checks whether any given word $w$ can we written as $w=uv$ with $u \in L_A$ and $v \in L_B$?


   Broad hint: how many possible choices for $u$ and $v$ are there?