What's There to Rationalize?

Algebra Level 2

yx2+1+xy2+1\dfrac{y}{x^{2}+1} + \dfrac{x}{y^{2}+1}

If x=3+2x= \sqrt{3} + \sqrt{2} and y=32y= \sqrt{3} - \sqrt{2}, then the expression above can be simplified to the form abb \dfrac { a \sqrt b}{b} where a,ba,b are coprime positive integers with bb square-free.

What is the value of a+ba+b?

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