Question

\(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{4}{1-\sqrt{7}}\)

Answer 1

Lời giải:

\(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{4}{1-\sqrt{7}}\)

\(=\frac{\sqrt{12}-\sqrt{36}}{\sqrt{8}-\sqrt{24}}-\frac{\sqrt{3}(\sqrt{3}+1)}{\sqrt{3}}+\frac{4(1+\sqrt{7})}{(1-\sqrt{7})(1+\sqrt{7})}\)

\(=\frac{\sqrt{12}(1-\sqrt{3})}{\sqrt{8}(1-\sqrt{3})}-(\sqrt{3}+1)+\frac{4(1+\sqrt{7})}{1-7}\)

\(=\frac{\sqrt{6}}{2}-(\sqrt{3}+1)-\frac{2(1+\sqrt{7})}{3}\)