\(P=\frac{2\left(\sqrt{8}-\sqrt{3}\right)}{\sqrt{6}\left(\sqrt{3}-\sqrt{8}\right)}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)

\(=-\frac{2}{\sqrt{6}}-\frac{1}{\sqrt{6}}=\frac{-3}{\sqrt{6}}=-\frac{\sqrt{6}}{2}\)

Trả lời:

\(P=\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

\(P=\frac{2\sqrt{8}-2\sqrt{3}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

\(P=\frac{2.\left(\sqrt{8}-\sqrt{3}\right)}{\sqrt{6}.\left(\sqrt{3}-\sqrt{8}\right)}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{6}.\left(\sqrt{5}+\sqrt{27}\right)}\)

\(P=\frac{-2.\left(\sqrt{3}-\sqrt{8}\right)}{\sqrt{6}.\left(\sqrt{3}-\sqrt{8}\right)}-\frac{1}{\sqrt{6}}\)

\(P=\frac{-2}{\sqrt{6}}-\frac{1}{\sqrt{6}}\)

\(P=\frac{-3}{\sqrt{6}}\)

\(P=\frac{-\sqrt{6}}{2}\)

Học tốt 

\(-\frac{\sqrt{6}}{2}\)

tìm ĐKXĐ rồi đặt nhân tử chung rút gọn nêu rút gọn vẫn còn căn ở mẫu thì trục căn sau đó quy đồng giải bình thường

Ta có: \(P=\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

\(=\frac{2\left(\sqrt{8}-\sqrt{3}\right)}{-\sqrt{6}\left(\sqrt{8}-\sqrt{3}\right)}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)

\(=\frac{-\sqrt{2}}{\sqrt{3}}-\frac{1}{\sqrt{6}}\)

\(=\frac{-2-1}{\sqrt{6}}=\frac{-3}{\sqrt{6}}=\frac{-\sqrt{3}}{\sqrt{2}}\)