Question

Rút gọn: \(\sqrt{12}-\dfrac{3+\sqrt{3}}{\sqrt{3}+1}+\dfrac{11}{2\sqrt{3}+1}\)

Answer 1

Ta có: \(\sqrt{12}-\dfrac{3+\sqrt{3}}{\sqrt{3}+1}+\dfrac{11}{2\sqrt{3}+1}\)

\(=2\sqrt{3}-\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+\dfrac{11\left(2\sqrt{3}-1\right)}{\left(2\sqrt{3}+1\right)\left(2\sqrt{3}-1\right)}\)

\(=2\sqrt{3}-\sqrt{3}+\left(2\sqrt{3}-1\right)\)

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

\(=3\sqrt{3}-1\)

Answer 2

Ta có : \(\sqrt{12}-\dfrac{3+\sqrt{3}}{\sqrt{3}+1}+\dfrac{11}{2\sqrt{3}+1}\)

\(=\sqrt{12}-\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}+1}+\dfrac{\left(2\sqrt{3}+1\right)\left(2\sqrt{3}-1\right)}{2\sqrt{3}+1}\)

\(=\sqrt{12}-\sqrt{3}+2\sqrt{3}-1=2\sqrt{3}-\sqrt{3}+2\sqrt{3}-1\)

\(=3\sqrt{3}-1\)