c)
\frac{\sqrt{12}+2\sqrt{27}+4\sqrt{75}}{3\sqrt{48}+6\sqrt3}=\frac{\sqrt{4*3}+2\sqrt{9*3}+4\sqrt{25*3}}{3\sqrt{16*3}+6\sqrt3}=\frac{2\sqrt3+6\sqrt3+20\sqrt3}{12\sqrt3+6\sqrt3}=
\frac{28\sqrt3}{18\sqrt3}=\frac{14}{9}=1\frac{5}{9}
a)
\frac{2\sqrt{24}+\sqrt{150}+5\sqrt{216}}{12\sqrt6+9\sqrt{54}-4\sqrt{96}}=
\frac{2\sqrt{4*6}+\sqrt{25*6}+5\sqrt{36*6}}{12\sqrt6+9\sqrt{9*6}-4\sqrt{16*6}}=\frac{4\sqrt6+5\sqrt6+30\sqrt6}{12\sqrt6+27\sqrt6-16\sqrt6}=\frac{39\sqrt6}{13\sqrt6}=3
b)
\frac{\sqrt{28}-5\sqrt{63}-4\sqrt{175}}{6\sqrt7+3\sqrt{112}-5\sqrt{700}}=\frac{\sqrt{4*7}-5\sqrt{9*7}-4\sqrt{25*7}}{6\sqrt6+3\sqrt{16*7}-5\sqrt{100*7}}=
\frac{2\sqrt7-15\sqrt7-20\sqrt7}{6\sqrt7+12\sqrt7-50\sqrt7}=\frac{-33\sqrt7}{-32\sqrt7}=1\frac{1}{32}