7) \(\dfrac{6}{1-\sqrt{3}}-\dfrac{3\sqrt{3}+3}{\sqrt{3}+1}\)
\(=\dfrac{6\left(1+\sqrt{3}\right)}{\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)}-\dfrac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}\)
\(=\dfrac{6\left(1+\sqrt{3}\right)}{1-3}-3\)
\(=\dfrac{6\left(1+\sqrt{3}\right)}{-2}-3\)
\(=-3\left(1+\sqrt{3}\right)-3\)
\(=-3-3\sqrt{3}-3\)
\(=-6-3\sqrt{3}\)
8) \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}\)
\(=\dfrac{\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}+\dfrac{6\left(2+\sqrt{10}\right)}{\left(2-\sqrt{10}\right)\left(2+\sqrt{10}\right)}\)
\(=\sqrt{10}+\dfrac{6\left(2+\sqrt{10}\right)}{4-10}\)
\(=\sqrt{10}+\dfrac{6\left(2+\sqrt{10}\right)}{-6}\)
\(=\sqrt{10}-2-\sqrt{10}\)
\(=-2\)
9) \(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}+\dfrac{3}{\sqrt{2}-\sqrt{5}}\)
\(=\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{1-\sqrt{5}}+\dfrac{3\left(\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}\)
\(=-\sqrt{5}+\dfrac{3\left(\sqrt{2}+\sqrt{5}\right)}{2-5}\)
\(=-\sqrt{5}+\dfrac{3\left(\sqrt{2}+\sqrt{5}\right)}{-3}\)
\(=-\sqrt{5}-\sqrt{2}-\sqrt{5}\)
\(=-2\sqrt{5}-\sqrt{2}\)
10) \(\dfrac{7}{3\sqrt{2}-5}-\dfrac{\sqrt{18}-3\sqrt{6}}{\sqrt{3}-1}\)
\(=\dfrac{7\left(3\sqrt{2}+5\right)}{\left(3\sqrt{2}-5\right)\left(3\sqrt{2}+5\right)}+\dfrac{\sqrt{18}\left(1-\sqrt{3}\right)}{\sqrt{3}-1}\)
\(=\dfrac{7\left(3\sqrt{2}+5\right)}{18-25}-\sqrt{18}\)
\(=-\left(3\sqrt{2}+5\right)-\sqrt{18}\)
\(=-3\sqrt{2}-5-3\sqrt{2}\)
\(=-6\sqrt{2}-5\)
7: \(=-3\left(\sqrt{3}+1\right)-3=-3\sqrt{3}-3-3=-3\sqrt{3}-6\)
8: \(=\dfrac{\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}-\sqrt{10}-\sqrt{2}\)
=căn 10-căn 10-căn 2
=-căn 2
9: \(=-\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}-\sqrt{5}-\sqrt{2}\)
=-căn 5-căn 5-căn 2
=-2căn 5-căn 2
10: \(=-5-3\sqrt{2}+3\sqrt{2}=-5\)
