Question

Answer 1

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

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

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

\(=\dfrac{4}{3-4}\cdot\sqrt{2}\)

\(=-4\sqrt{2}\)

Answer 2

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

\(=-4\sqrt{2}\)