\(\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}-1}\) - \(\frac{3\sqrt{5}+5}{\sqrt{5}+3}\)+ \(\frac{2}{\sqrt{2}}\)
= \(\frac{\left(\sqrt{10}-\sqrt{5}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}\)- \(\frac{\left(3\sqrt{5}+5\right)\left(3-\sqrt{5}\right)}{\left(\sqrt{5}+3\right)\left(3-\sqrt{5}\right)}\)+ \(\sqrt{2}\)
= \(\frac{\sqrt{20}-\sqrt{10}+\sqrt{10}-\sqrt{5}}{2-1}\)- \(\frac{9\sqrt{5}-3.5+15-5\sqrt{5}}{9-5}+\sqrt{2}\)
= \(2\sqrt{5}-\sqrt{5}-\frac{4\sqrt{5}}{4}+\sqrt{2}\)
= \(2\sqrt{5}-\sqrt{5}-\sqrt{5}+\sqrt{2}\)
= \(0\sqrt{5}+\sqrt{2}\)
= \(0+\sqrt{2}\)
= \(\sqrt{2}\)
cách 2 : theo cách rút gọn
= \(\sqrt{5}-\frac{3\sqrt{5}+5}{\sqrt{5}+3}+\frac{2}{\sqrt{2}}\)
= \(\sqrt{5}-\frac{\sqrt{5}}{1}+\frac{2}{\sqrt{2}}\)
= \(\sqrt{5}-\frac{\sqrt{5}}{1}+\sqrt{2}\)
= \(\frac{\sqrt{5}}{1}-\frac{\sqrt{5}}{1}+\sqrt{2}\)
= \(\sqrt{2}\)
