Giải thích các bước giải:
Ta có:
$(\dfrac{1}{5-2\sqrt{6}}+\dfrac{2}{5+2\sqrt{6}})(15+2\sqrt{6})$
$=\dfrac{5+2\sqrt{6}+2(5-2\sqrt{6})}{(5-2\sqrt{6})(5+2\sqrt{6})}\cdot (15+2\sqrt{6})$
$=\dfrac{15-2\sqrt{6}}{5^2-(2\sqrt{6})^2}\cdot (15+2\sqrt{6})$
$=\dfrac{15-2\sqrt{6}}{1}\cdot (15+2\sqrt{6})$
$=(15-2\sqrt{6})\cdot (15+2\sqrt{6})$
$=15^2-(2\sqrt{6})^2$
$=225-24$
$=201$