\(\dfrac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\dfrac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\dfrac{\left(\sqrt{5}-2\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\dfrac{\left(2\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{5-\sqrt{15}-2\sqrt{15}+6}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\dfrac{10+2\sqrt{15}+\sqrt{15}+3}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{11-3\sqrt{15}-13-3\sqrt{15}}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{-2-6\sqrt{15}}{5-3}=\dfrac{-2\left(1+3\sqrt{15}\right)}{2}=-\left(1+3\sqrt{15}\right)=-1-3\sqrt{15}\)
nhân tử vs mẫu vs \(\sqrt{5}-\sqrt{3}\)
và nhân tử vs mẫu vs\(\sqrt{5}-\sqrt{3}\)