rozwiązania
a)
\frac{3\sqrt7}{2\sqrt3}=\frac{3\sqrt7*\sqrt3}{2\sqrt3*\sqrt3}=\frac{\not3^1\sqrt{21}}{2*\not3^1}=\frac{\sqrt{21}}{2}
b)
{\frac{8-\sqrt2}{5\sqrt2}=\frac{\sqrt2(8-\sqrt2)}{5\sqrt2*\sqrt2}=\frac{8\sqrt2-(\sqrt2)^2}{5*2}=\frac{8\sqrt2-2}{10}=\frac{\not2^1(4\sqrt2-1)}{\not10^5}=\frac{4\sqrt2-1}{5}}
c)
\frac{\sqrt3-\sqrt{13}}{3\sqrt{13}}=\frac{(\sqrt3-\sqrt{13})*\sqrt{13}}{3\sqrt{13}*\sqrt{13}}=\frac{\sqrt{39}-13}{3*13}=\frac{\sqrt{39}-13}{39}
d)
\frac{3}{4-\sqrt3}=\frac{3(4+\sqrt3)}{(4-\sqrt3)(4+\sqrt3)}=\frac{3(4+\sqrt3)}{4^2-(\sqrt3)^2}=\frac{3(4+\sqrt3)}{16-3}=\frac{3(4+\sqrt3)}{13}
lub
=\frac{12+3\sqrt3}{13}
e)
\frac{2\sqrt5}{\sqrt3+\sqrt7}=\frac{2\sqrt5(\sqrt3-\sqrt7)}{(\sqrt3+\sqrt7)(\sqrt3-\sqrt7)}=\frac{2\sqrt{15}-2\sqrt{35}}{(\sqrt3)^2-(\sqrt7)^2}=\frac{2\sqrt{15}-2\sqrt{35}}{3-7}=
\frac{\not2^1(\sqrt{15}-\sqrt{35})}{-\not4^2}=\frac{\sqrt{15}-\sqrt{35}}{-2}=\frac{-(\sqrt{15}-\sqrt{35})}{2}=\frac{\sqrt{35}-\sqrt{15}}{2}
f)
\frac{3\sqrt3+2\sqrt5}{3\sqrt5-2\sqrt2}=\frac{(3\sqrt3+2\sqrt5)(3\sqrt5+2\sqrt2)}{(3\sqrt5-2\sqrt2)(3\sqrt5+2\sqrt2)}=\frac{9\sqrt{15}+6\sqrt6+6*5+4\sqrt{10}}{(3\sqrt5)^2-(2\sqrt2)^2}=
=\frac{9\sqrt{15}+4\sqrt{10}+6\sqrt6+30}{9*5-4*2}=\frac{9\sqrt{15}+4\sqrt{10}+6\sqrt6+30}{37}