\(\left(\dfrac{3}{\sqrt{2}+1}+\dfrac{14}{2\sqrt{2}-1}-\dfrac{4}{2-\sqrt{2}}\right)\left(\sqrt{8}+2\right)=\left[\dfrac{3}{\sqrt{2}+1}+\dfrac{14}{\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)}-\dfrac{4}{\sqrt{2}\left(\sqrt{2}-1\right)}\right]\left(\sqrt{8}+2\right)=\left[\dfrac{3}{\sqrt{2}+1}+\dfrac{14-2\sqrt{2}\left(3+\sqrt{2}\right)}{\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)}\right]\left(\sqrt{2}+1\right).2=\left[\dfrac{3}{\sqrt{2}+1}+\dfrac{14-6\sqrt{2}-4}{\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)}\right]\left(\sqrt{2}+1\right).2=\dfrac{3\left(2\sqrt{2}-1\right)+\left(10-6\sqrt{2}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)}.2\left(\sqrt{2}+1\right)=\dfrac{6\sqrt{2}-3+10\sqrt{2}+10-12-6\sqrt{2}}{2\sqrt{2}-1}.2=\dfrac{10\sqrt{2}-5}{\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)}.2=\dfrac{5\left(2\sqrt{2}-1\right)}{2\sqrt{2}-1}.2=5.2=10\)
