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.

What is the value of $a+b$ ?