What's There to Rationalize?

Algebra Level 2

\[\dfrac{y}{x^{2}+1} + \dfrac{x}{y^{2}+1}\]

If \(x= \sqrt{3} + \sqrt{2}\) and \(y= \sqrt{3} - \sqrt{2}\), then the expression above can be simplified to the form \( \dfrac { a \sqrt b}{b} \) where \(a,b\) are coprime positive integers with \(b\) square-free.