BẠN THAM KHẢO NHA!
Đáp án:
$=\dfrac{2+2\sqrt{2}-\sqrt{5}}{2}$
Giải thích các bước giải:
$\dfrac{\sqrt{10}-\sqrt{5}}{\sqrt{2}-1}-\dfrac{3\sqrt{5}+3}{\sqrt{5}+3}+\dfrac{2}{\sqrt{2}}$
$=\dfrac{\sqrt{5}.(\sqrt{2}-1)}{\sqrt{2}-1}-\dfrac{(3\sqrt{5}+3)(\sqrt{5}-3)}{(\sqrt{5}+3)(\sqrt{5}-3)}+\dfrac{2\sqrt{2}}{2}$
$=\sqrt{5}-\dfrac{15-9\sqrt{5}+3\sqrt{5}-9}{5-9}+\dfrac{2\sqrt{2}}{2}$
$=\dfrac{2\sqrt{5}}{2}+\dfrac{6-6\sqrt{5}}{4}+\dfrac{2\sqrt{2}}{2}$
$=\dfrac{2\sqrt{5}+3-3\sqrt{5}+2\sqrt{2}}{2}$
$=\dfrac{2+2\sqrt{2}-\sqrt{5}}{2}$
