a) \(=\dfrac{2\sqrt{2}-\sqrt{7}}{8-7}+5\sqrt{7}-\dfrac{2\sqrt{2}\left(3-\sqrt{2}\right)}{3-\sqrt{2}}\)
\(=2\sqrt{2}-\sqrt{7}+5\sqrt{7}-2\sqrt{2}=4\sqrt{7}\)
b) \(=8\sqrt{6}-\sqrt{6}-5\sqrt{6}=2\sqrt{6}\)
c) \(=\sqrt{\left(2\sqrt{5}-3\right)^2}-\sqrt{\left(3-\sqrt{5}\right)^2}=2\sqrt{5}-3-3+\sqrt{5}=-6+3\sqrt{5}\)
d) \(=\dfrac{2\sqrt{3}-3+2\sqrt{3}+3}{12-9}=\dfrac{4\sqrt{3}}{3}\)
e) \(=\dfrac{\sqrt{3}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}-\dfrac{2\left(\sqrt{3}+1\right)}{3-1}=\sqrt{3}-\sqrt{3}-1=-1\)
b: \(\dfrac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}-\dfrac{2}{\sqrt{3}-1}\)
\(=\sqrt{3}-\sqrt{3}-1\)
=-1
