Question

\(\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{3-\sqrt[]{3}}{2\sqrt[]{3}-2}+\frac{\sqrt[]{6}+\sqrt[]{3}}{2\sqrt[]{2}+2}\)

Answer 1

\(\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{3-\sqrt{3}}{2\sqrt{3}-2}+\frac{\sqrt{6}+\sqrt{3}}{2\sqrt{2}+2}\)

=\(\frac{\left(2+\sqrt{2}\right)\cdot\left(1-\sqrt{2}\right)}{\left(1+\sqrt{2}\right)\cdot\left(1-\sqrt{2}\right)}-\frac{\left(3-\sqrt{3}\right)\cdot\left(2\sqrt{3}+2\right)}{\left(2\sqrt{3}-2\right)\cdot\left(2\sqrt{3}+2\right)}+\frac{\left(\sqrt{6}+\sqrt{3}\right)\cdot\left(2\sqrt{2}-2\right)}{\left(2\sqrt{2}+2\right)\cdot\left(2\sqrt{2}-2\right)}\)

=\(\frac{-\sqrt{2}}{-1}-\frac{4\sqrt{3}}{8}+\frac{2\sqrt{3}}{4}\)

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

=\(\sqrt{2}\)