\(A=\dfrac{1}{2\sqrt{2}}-\dfrac{2}{\sqrt{2}+1}-\dfrac{7}{2\sqrt{2}+4}\)
\(=\dfrac{\sqrt{2}}{4}-2\left(\sqrt{2}-1\right)-\dfrac{7\left(2\sqrt{2}-4\right)}{-8}\)
\(=\dfrac{\sqrt{2}}{4}-2\sqrt{2}+2-\dfrac{7\cdot2\left(\sqrt{2}-2\right)}{-8}\)
\(=-\dfrac{7\sqrt{2}}{4}+2-\dfrac{7\left(\sqrt{2}-2\right)}{-4}\)
\(=-\dfrac{7\sqrt{2}}{4}+2-\dfrac{7\sqrt{2}-14}{-4}\)
\(=-\dfrac{7\sqrt{2}}{4}+2-\dfrac{7\sqrt{2}-14}{4}\)
\(=\dfrac{-7\sqrt{2}+7\sqrt{2}-14}{4}+2\)
\(=-\dfrac{14}{4}+2\)
\(=-\dfrac{3}{2}\)
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