Lần sau bạn chú ý ghi đầy đủ đề.
Lời giải:
\(A=\frac{2\sqrt{3}-6}{2-2\sqrt{3}}-\frac{\sqrt{3}(1-\sqrt{3})}{\sqrt{3}}+\frac{4(1+\sqrt{3})}{(1-\sqrt{3})(1+\sqrt{3})}\)
\(=\frac{2\sqrt{3}(1-\sqrt{3})}{2(1-\sqrt{3})}-(1-\sqrt{3})+\frac{4(1+\sqrt{3})}{1-3}\)
\(=\sqrt{3}-1+\sqrt{3}-2(1+\sqrt{3})=-3\)
\(\dfrac{\sqrt{12}-6}{2-\sqrt{12}}-\dfrac{\sqrt{3}-3}{\sqrt{3}}+\dfrac{4}{1-\sqrt{3}}\)
\(=\dfrac{\sqrt{12}\left(1-\sqrt{3}\right)}{\sqrt{4}\left(1-\sqrt{3}\right)}-\sqrt{3}+\dfrac{4\left(1+\sqrt{3}\right)}{1-3}\)
\(=\sqrt{3}-\sqrt{3}+4+4\sqrt{3}=4\sqrt{3}+4\)
Ta có: \(\dfrac{\sqrt{12}-6}{2-\sqrt{12}}-\dfrac{\sqrt{3}-3}{\sqrt{3}}+\dfrac{4}{1-\sqrt{3}}\)
\(=\dfrac{2\sqrt{3}\left(1-\sqrt{3}\right)}{2\left(1-\sqrt{3}\right)}+\dfrac{3-\sqrt{3}}{\sqrt{3}}-\dfrac{4\left(\sqrt{3}+1\right)}{2}\)
\(=\sqrt{3}+\sqrt{3}-1-2\left(\sqrt{3}+1\right)\)
\(=2\sqrt{3}-1-2\sqrt{3}-2\)
=-3
