Question

Thực hiện phép tính sau:

a) \(\dfrac{8+2\sqrt{2}}{3-\sqrt{2}}-\dfrac{2+3\sqrt{2}}{\sqrt{2}}+\dfrac{\sqrt{2}}{1-\sqrt{2}}\)

Answer 1

\(\dfrac{8+2\sqrt{2}}{3-\sqrt{2}}-\dfrac{2+3\sqrt{2}}{\sqrt{2}}+\dfrac{\sqrt{2}}{1-\sqrt{2}}\)

\(=\dfrac{\left(8+2\sqrt{2}\right)\left(3+\sqrt{2}\right)}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}-\dfrac{\sqrt{2}\left(\sqrt{2}+3\right)}{\sqrt{2}}-\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}\)

\(=\dfrac{24+14\sqrt{2}+4}{9-2}-\dfrac{\sqrt{2}+3}{1}-\dfrac{2+\sqrt{2}}{2-1}\)

\(=\dfrac{28+14\sqrt{2}}{7}-\sqrt{2}-3-2-\sqrt{2}\)

\(=4+2\sqrt{2}-\sqrt{2}-3-2-\sqrt{2}\)

\(=-1\)