1) $\dfrac{\sqrt{10}+\sqrt6}{\sqrt5+\sqrt3}+\dfrac{\sqrt6+\sqrt3}{\sqrt2+1}-\dfrac{3-\sqrt6}{\sqrt3}$

$=\dfrac{\sqrt2(\sqrt5+\sqrt3)}{\sqrt5+\sqrt3}+\dfrac{\sqrt3(\sqrt2+1)}{\sqrt2+1}-\dfrac{\sqrt3(\sqrt3-\sqrt2)}{\sqrt3}$

$=\sqrt2+\sqrt3-(\sqrt3-\sqrt2)=2\sqrt2$

2) $\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt5-2}-\dfrac{3\sqrt6}{\sqrt2}+\dfrac{3+\sqrt6}{\sqrt3+\sqrt2}$

$=\dfrac{\sqrt3(\sqrt5-2)}{\sqrt5-2}-\dfrac{3\sqrt3\sqrt2}{\sqrt2}+\dfrac{\sqrt3(\sqrt3+\sqrt2)}{\sqrt3+\sqrt2}$

$=\sqrt3-3\sqrt3+\sqrt3$

$=-\sqrt3$

5) $\dfrac{2\sqrt3-3\sqrt2}{\sqrt6}-\dfrac{2-\sqrt2}{1-\sqrt2}-\dfrac{3}{\sqrt3}$

$=\dfrac{\sqrt2\sqrt2\sqrt3-\sqrt3\sqrt3\sqrt2}{\sqrt6}-\dfrac{\sqrt2(\sqrt2-1)}{1-\sqrt2}-\dfrac{\sqrt3\sqrt3}{\sqrt3}$

$=\dfrac{\sqrt6(\sqrt2-\sqrt3)}{\sqrt6}+\dfrac{\sqrt2(1-\sqrt2)}{1-\sqrt2}-\sqrt3$

$=\sqrt2-\sqrt3+\sqrt2-\sqrt3$

$=2\sqrt2-2\sqrt3$

3) $\dfrac{3+2\sqrt3}{\sqrt3}+\dfrac{2+\sqrt2}{\sqrt2+1}-\dfrac{1}{2-\sqrt3}$

$\dfrac{\sqrt3(\sqrt3+2)}{\sqrt3}+\dfrac{\sqrt2(\sqrt2+1)}{\sqrt2+1}-\dfrac{1}{2-\sqrt3}$

$=\sqrt3+2+\sqrt2-\dfrac{1}{2-\sqrt3}$

$=\dfrac{(\sqrt3+2+\sqrt2)(2-\sqrt3)}{2-\sqrt3}$

$=\dfrac{2\sqrt3-3+4-2\sqrt3+2\sqrt2-\sqrt6}{2-\sqrt3}$

$=\dfrac{1+2\sqrt2-\sqrt6}{2-\sqrt3}$

7) $\left({\dfrac{\sqrt6-\sqrt3}{\sqrt2-1}+\dfrac{\sqrt6-\sqrt2}{\sqrt3-1}}\right):\dfrac{1}{\sqrt3-\sqrt2}$

$=\left({\dfrac{\sqrt3(\sqrt2-1)}{\sqrt2-1}+\dfrac{\sqrt2(\sqrt3-1)}{\sqrt3-1}}\right):\dfrac{1}{\sqrt3-\sqrt2}$

$=(\sqrt3+\sqrt2).(\sqrt3-\sqrt2)$

$=3-2$

$=1$

8) $\left({\dfrac{\sqrt{14}-\sqrt7}{1-\sqrt2}+\dfrac{\sqrt{15}-\sqrt5}{1-\sqrt3}}\right):\dfrac{1}{\sqrt7-\sqrt5}$

$=\left({\dfrac{\sqrt7(\sqrt2-1)}{1-\sqrt2}+\dfrac{\sqrt5(\sqrt3-1)}{1-\sqrt3}}\right):\dfrac{1}{\sqrt7-\sqrt5}$

$=(-\sqrt7-\sqrt5)(\sqrt7-\sqrt5)$

$=-(7-5)$

$=-2$

10) $\left({\dfrac{2\sqrt2-1}{\sqrt2-1}+\sqrt2}\right)\left({\dfrac{2\sqrt2+1}{\sqrt2+1}-\sqrt2}\right)$

$\left[{\dfrac{(\sqrt2-1)(2+\sqrt2+1)}{\sqrt2-1}+\sqrt2}\right]\left[{\dfrac{(\sqrt2+1)(2-\sqrt2+1)}{\sqrt2+1}-\sqrt2}\right]$

$=(2+\sqrt2+1+\sqrt2)(2-\sqrt2+1-\sqrt2)$

$=(3+2\sqrt2)(3-2\sqrt2)$

$=9-8$

$=1$