[tex]\displaystyle\bf\\1)\\\\\frac{5+a}{5^{\frac{1}{3} } +a^{\frac{1}{3} } } =\frac{(5^{\frac{1}{3} })^{3} +(a^{\frac{1}{3} } )^{3} }{5^{\frac{1}{3} } +a^{\frac{1}{3} } } =\frac{(5^{\frac{1}{3} } +a^{\frac{1}{3} } )\cdot(5^{\frac{2}{3} }-5^{\frac{1}{3} } a^{\frac{1}{3} } +a^{\frac{2}{3} }) }{5^{\frac{1}{3} } +a^{\frac{1}{3} } } =\\\\\\=5^{\frac{2}{3} } -5^{\frac{1}{3} } a^{\frac{1}{3} } +a^{\frac{2}{3} } \\\\2)\\\\\frac{a^{\frac{1}{2} } +1}{a+a^{\frac{1}{2} } +1} :\frac{1}{a^{\frac{3}{2} } -1} =[/tex]

[tex]\displaystyle\bf\\=\frac{a^{\frac{1}{2} } +1}{a+a^{\frac{1}{2} } +1} :\frac{1}{(a^{\frac{1}{2} })^{3} -1^{3} } =\frac{a^{\frac{1}{2} } +1}{a+a^{\frac{1}{2} } +1} \cdot(a^{\frac{1}{2} } -1)\cdot(a+a^{\frac{1}{2} } +1)=\\\\\\=(a^{\frac{1}{2} } +1)\cdot(a^{\frac{1}{2} } -1)=(a^{\frac{1}{2} } )^{2} -1^{2}=a-1\\\\\\a=2 \ \ \Rightarrow \ \ a-1=2-1=1\\\\\\Otvet \ : \ 1[/tex]