\(\left(\dfrac{2\sqrt{2}+3\sqrt{3}}{\sqrt{2}+\sqrt{3}}-\sqrt{6}\right):\left(\sqrt{2}-\sqrt{3}\right)-\dfrac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}=\left[\dfrac{\left(\sqrt{2}+\sqrt{3}\right)\left(2-\sqrt{6}+3\right)}{\sqrt{2}+\sqrt{3}}-\sqrt{6}\right].\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{2\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}=\left(5-\sqrt{6}-\sqrt{6}\right).\dfrac{1}{\sqrt{2}-\sqrt{3}}+2\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)=\dfrac{5-2\sqrt{6}}{\sqrt{2}-\sqrt{3}}+2\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)=\dfrac{5-2\sqrt{6}+2\sqrt{6}\left(\sqrt{2}-\sqrt{3}\right)^2}{\sqrt{2}-\sqrt{3}}=\dfrac{5-2\sqrt{6}+2\sqrt{6}\left(2-2\sqrt{6}+3\right)}{\sqrt{2}-\sqrt{3}}=\dfrac{5-2\sqrt{6}+2\sqrt{6}\left(5-2\sqrt{6}\right)}{\sqrt{2}-\sqrt{3}}=\dfrac{5-2\sqrt{6}+10\sqrt{6}-24}{\sqrt{2}-\sqrt{3}}=\dfrac{8\sqrt{6}-19}{\sqrt{2}-\sqrt{3}}=\dfrac{\left(8\sqrt{6}-19\right)\left(\sqrt{2}+\sqrt{3}\right)}{2-3}=-\left(16\sqrt{3}+24\sqrt{2}-19\sqrt{2}-19\sqrt{3}\right)=-\left(5\sqrt{2}-3\sqrt{3}\right)=3\sqrt{3}-5\sqrt{2}\)
nghĩ nát óc,cuối cùng Mk cũng làm đc câu này. Mọi người xem thử mk làm có đúng k nha !
(\(\dfrac{2\sqrt{2}+3\sqrt{3}}{\sqrt{2}+\sqrt{3}}\)\(-\sqrt{6}\) ):(\(\sqrt{2}-\sqrt{3}\))-\(\dfrac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)
nhân liên hợp.Phần này viết lại dài quá tớ ghi luôn thế này , kết quả tớ rút gọn luôn nha :
=(-4+2\(\sqrt{6}\)+3\(\sqrt{6}\)\(+9-\sqrt{6}\)).\(\dfrac{1}{\sqrt{2}-\sqrt{3}}\)+2\(\sqrt{6}\)\(\left(\sqrt{2}-\sqrt{3}\right)\)
= \(5-2\sqrt{6}\).\(\dfrac{1}{\sqrt{2}-\sqrt{3}}\)+2\(\sqrt{6}\)\(\left(\sqrt{2}-\sqrt{3}\right)\)
=\(\left(\sqrt{2}-\sqrt{3}\right)^2\).\(\dfrac{1}{\sqrt{2}-\sqrt{3}}\)+2\(\sqrt{6}\)\(\left(\sqrt{2}-\sqrt{3}\right)\)
=\(\left(\sqrt{2}-\sqrt{3}\right)\)+2\(\sqrt{6}\)\(\left(\sqrt{2}-\sqrt{3}\right)\)
=\(\left(\sqrt{2}-\sqrt{3}\right)\)\(\left(1+2\sqrt{6}\right)\)
=\(4\sqrt{3}-6\sqrt{2}\)
