Question

rút gọn biểu thức

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

Answer 1

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

Answer 2

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

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

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

\(=-\left(2-2\sqrt{2}+\sqrt{2}-2\right)\)

\(=-\left(-\sqrt{2}\right)\)

\(=\sqrt{2}\)