Verified answer

[tex]\displaystyle\bf\\\frac{1}{1-4\sqrt{5} } =\frac{1\cdot(1+4\sqrt{5} )}{(1-4\sqrt{5} )\cdot(1+4\sqrt{5} )} =\frac{1+4\sqrt{5} }{1^{2} -(4\sqrt{5} )^{2} } =\\\\\\=\frac{1+4\sqrt{5} }{1-80}=-\frac{1+4\sqrt{5} }{79}[/tex]