Rút gọn căn thức ạa, giúp em với

Giải thích các bước giải:

$a) \dfrac{4}{\sqrt{3}-1} + \dfrac{7}{3-\sqrt{2}} - 2\sqrt{3}$

$= \dfrac{4(\sqrt{3}+1)}{3-1} + \dfrac{7(3+\sqrt{2})}{9-2} - 2\sqrt{3}$

$= \dfrac{4(\sqrt{3}+1)}{2} + \dfrac{7(3+\sqrt{2})}{7} - 2\sqrt{3}$

$= 2(\sqrt{3}+1) + (3+\sqrt{2}) - 2\sqrt{3}$

$= 2\sqrt{3} + 2 + 3 + \sqrt{2} - 2\sqrt{3}$

$= 5 + \sqrt{2}$

$b) \dfrac{5}{\sqrt{3}-\sqrt{15}} - \dfrac{4}{\sqrt{5}-3}$

$= \dfrac{5(\sqrt{3}+\sqrt{15})}{3-15} - \dfrac{4(\sqrt{5}+3)}{5-9}$

$= \dfrac{5\sqrt{3}+5\sqrt{15}}{-12} - \dfrac{4(\sqrt{5}+3)}{-4}$

$= \dfrac{-5\sqrt{3}-5\sqrt{15}}{12} + (\sqrt{5}+3)$

$= \dfrac{-5\sqrt{3}-5\sqrt{15}+12\sqrt{5}+36}{12}$