Question

Rút gọn biểu thức

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

Answer 1

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

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

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

\(=\dfrac{2}{1-2}\)

\(=-2\)

Answer 2

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