[tex] \frac{4}{5 + \sqrt{5} } [/tex]

[tex] \frac{4}{5+ \sqrt{5} } = \frac{4}{5+ \sqrt{5} } \times \frac{5- \sqrt{5}}{5- \sqrt{5} }= \frac{4(5- \sqrt{5})}{25-5} =\frac{4(5- \sqrt{5})}{20} =\frac{5- \sqrt{5}}{5} =1- \frac{1}{5} \sqrt{5} [/tex]