looking for some shortcut or faster method for solving a question involving square root If $x =\dfrac{ \sqrt 3 - \sqrt 2 }{ \sqrt 3 + \sqrt 2 } $ and $ y = \dfrac{\sqrt 3 + \sqrt 2 }{ \sqrt 3 - \sqrt 2}$, find the value of 
$\dfrac{x^2 + xy + y^2}{x^2 - xy + y^2}.$

I obviously know the traditional method of solving this qn (by multiplying by conjugate).  I want to know if there is some faster method to solve this question.
Use $$x^2+xy+y^2=(x+y)^2-xy$$ and $$x^2-xy+y^2=(x-y)^2+xy$$ and you can easily find $x+y,x-y,xy$

Complete solution:
$$x=5-2√6$$
$$y=5+2√6$$
$$xy=1$$
Answer=$$\frac{10^2-1}{(-4√6)^2+1}$$$$=\frac{99}{97}$$
$$\implies xy=1$$

and $$x=\dfrac{(\sqrt3-\sqrt2)^2}{3-2}=5-2\sqrt6$$

Similarly, $y=5+2\sqrt6$

$$x^2+xy+y^2=(x+y)^2-xy=?$$