[tex]\dfrac{2\sqrt{27}+\sqrt{75}}{\sqrt{12}} = \dfrac{2\sqrt{9\cdot3}+\sqrt{25\cdot3}}{\sqrt{4\cdot3}} = \dfrac{2\cdot\sqrt{9}\cdot\sqrt{3}+\sqrt{25}\cdot\sqrt{3}}{\sqrt{4}\cdot\sqrt{3}}=\dfrac{2\cdot3\cdot\sqrt{3}+5\cdot\sqrt{3}}{2\cdot\sqrt{3}} =\\\\\\= \dfrac{6\sqrt{3}+5\sqrt{3}}{2\sqrt{3}} = \dfrac{11\sqrt{3}}{2\sqrt{3}} = \dfrac{11}{2} =5\dfrac{1}{2}[/tex]
