RO-TST 2012 Problem 3

Let $A$ and $B$ be finite sets of real numbers and let $x$ be an element of $A+B$ . Prove that $$|A\cap (x-B)|\leq \frac{|A-B|^2}{|A+B|}$$ where $A+B=\{a+b: a\in A, b\in B\}$ , $x-B=\{x-b: b\in B\}$ and $A-B=\{a-b: a\in A, b\in B\}$ .