Fraction problem

Assuming $x,y \in \mathbb{N},$ we have $\large \frac{1}{x} + \frac{1}{y} = \frac{4}{7} \Rightarrow \frac{x+y}{xy} = \frac{4}{7} \Rightarrow x = \frac{7y}{4y-7}$ . This fraction is solvable in the positive integers for $x = 14, y = 2$ , which yields: $x^2-y^2 = 14^2-2^2 = \boxed{192}.$