a)[latex] frac{5}{3 sqrt{10} } = frac{5 sqrt{10} }{3 sqrt{10} sqrt{10} } = frac{5 sqrt{10} }{3*10} = frac{ sqrt{10} }{6} [/latex]b) [latex] frac{8}{ sqrt{6}+ sqrt{2} } = frac{8 (sqrt{6}- sqrt{2} ) }{( sqrt{6}+ sqrt{2})( sqrt{6}- sqrt{2})}= frac{8 (sqrt{6}- sqrt{2} )}{6-2}= frac{8 (sqrt{6}- sqrt{2} )}{4} = 2( sqrt{6} - sqrt{2} )[/latex]

[latex]a) frac{5}{3sqrt{10}}=frac{5sqrt{10}}{3sqrt{10}ulletsqrt{10}}=frac{5sqrt{10}}{3(sqrt{10})^2}=frac{5sqrt{10}}{3ullet10}=frac{sqrt{10}}{6};\\b) frac{8}{sqrt{6}+sqrt2}=frac{8(sqrt6-sqrt2)}{(sqrt6+sqrt2)(sqrt6-sqrt2)}=frac{8(sqrt6-sqrt2)}{(sqrt{6})^2-(sqrt{2})^2}=frac{8(sqrt6-sqrt2)}{6-2}=\\=2(sqrt{3ullet2}-sqrt2)=2(sqrt2sqrt3-sqrt2)=2sqrt2(sqrt3-1).[/latex]