Question

\(\dfrac{\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}\)

Trục căn thức ở mẫu;

 

Answer 1

\(\dfrac{\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}=\dfrac{\sqrt{2}\left(1+\sqrt{2}+\sqrt{3}\right)}{\left(1+\sqrt{2}\right)^2-3}\)  = \(\dfrac{\sqrt{2}\left(1+\sqrt{2}+\sqrt{3}\right)}{1+2+2\sqrt{2}-3}=\dfrac{1+\sqrt{2}+\sqrt{3}}{2}\)

Answer 2

\(\dfrac{\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}=\dfrac{\sqrt{2}\left(1+\sqrt{2}+\sqrt{3}\right)}{\left(1+\sqrt{2}\right)^2-3}=\dfrac{\sqrt{2}+2+\sqrt{6}}{1+2\sqrt{2}+2-3}=\dfrac{\sqrt{2}+2+\sqrt{6}}{2\sqrt{2}}=\dfrac{2+2\sqrt{2}+2\sqrt{3}}{4}=\dfrac{1+\sqrt{2}+\sqrt{3}}{2}\)