[tex](a^{-1}+a^{-2})^{-1}=(\frac{1}{a}+\frac{1}{a^2})^{-1}=(\frac{a}{a^2}+\frac{1}{a^2})^{-1}=(\frac{a+1}{a^2})^{-1}=\frac{a^2}{a+1}\\\\\frac{(\sqrt7-1)^2}{\sqrt7+1-1}=\frac{7-2\sqrt7+1}{\sqrt7}=\frac{-2\sqrt7+8}{\sqrt7}=\frac{\sqrt7(-2\sqrt7+8)}{7}=\frac{-14+8\sqrt7}{7}[/tex]
