\(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\sqrt{8-2\sqrt{7}}+\sqrt{2}\)
\(=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)}-\sqrt{8-2\sqrt{7}}+\sqrt{2}\)
\(=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{7-2}-\sqrt{\left(\sqrt{7}\right)^2-2\cdot\sqrt{7}\cdot1+1^2}+\sqrt{2}\)
\(=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{5}-\sqrt{\left(\sqrt{7}-1\right)^2}+\sqrt{2}\)
\(=\left(\sqrt{7}-\sqrt{2}\right)-\left|\sqrt{7}-1\right|+\sqrt{2}\)
\(=\sqrt{7}-\sqrt{2}-\sqrt{7}+1+\sqrt{2}\)
\(=1\)
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