Question

Answer 1

Answer 2

\(=\left[\dfrac{3\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}+\dfrac{14\left(2\sqrt{2}+1\right)}{\left(2\sqrt{2}-1\right)\left(2\sqrt{2}+1\right)}-\dfrac{4\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}\right]\left(2\sqrt{2}+2\right)\)
\(=\left[\dfrac{3\sqrt{2}-3}{2-1}+\dfrac{14\left(2\sqrt{2}+1\right)}{8-1}-\dfrac{4\left(2+\sqrt{2}\right)}{4-2}\right]\left(2\sqrt{2}+2\right)\)
\(=\left[3\sqrt{2}-3+2\left(2\sqrt{2}+1\right)-2\left(2+\sqrt{2}\right)\right]\left(2\sqrt{2}+2\right)\)
\(=\left(3\sqrt{2}-3+4\sqrt{2}+2-4-2\sqrt{2}\right)\left(2\sqrt{2}+2\right)\)
\(=\left(5\sqrt{2}-5\right)\left(2\sqrt{2}+2\right)\)
\(=5\left(\sqrt{2}-1\right).2\left(\sqrt{2}+1\right)\)
\(=5.2.\left(2-1\right)=10\)