Question

Tính:

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

Answer 1

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

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

\(=\sqrt{3}+2+2\sqrt{2}-2+2-\sqrt{2}-\sqrt{2}+\sqrt{3}\)

\(=2\sqrt{3}+2\)

Answer 2

`[3+2\sqrt{3}]/\sqrt{3}+[2+\sqrt{2}]/[\sqrt{2}+1]-(\sqrt{2}-\sqrt{3})`

`=[\sqrt{3}(\sqrt{3}+2)]/\sqrt{3}+[\sqrt{2}(\sqrt{2}+1)]/[\sqrt{2}+1]-\sqrt{2}+\sqrt{3}`

`=\sqrt{3}+2+\sqrt{2}-\sqrt{2}+\sqrt{3}`

`=2\sqrt{3}+2`