$\dfrac{x^{2}-2xy+y^{2}}{x^{2}-y^{2}}$

$=\dfrac{\left(x-y\right)^{2}}{\left(x-y\right)\left(x+y\right)} \ldots (2$分）

$=\dfrac{x-y}{x+y}$，$\ldots (4$分）

当$x=\sqrt{3}+1$，$y=\sqrt{3}-1$时，原式$=\dfrac{2}{2\sqrt{3}}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}$.

$\dfrac{x^{2}-2xy+y^{2}}{x^{2}-y^{2}}$

$=\dfrac{\left(x-y\right)^{2}}{\left(x-y\right)\left(x+y\right)} \ldots (2$分）

$=\dfrac{x-y}{x+y}$，$\ldots (4$分）

当$x=\sqrt{3}+1$，$y=\sqrt{3}-1$时，原式$=\dfrac{2}{2\sqrt{3}}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}$.