[tex] = \frac{(1 + \sqrt{5}) }{(3 + \sqrt{5}) } \\ [/tex]
[tex] = \frac{(1 + \sqrt{5}) }{(3 + \sqrt{5} )} \times \frac{(3 - \sqrt{5} )}{(3 - \sqrt{5}) } \\ [/tex]
[tex] = \frac{1(3 - \sqrt{5}) + \sqrt{5} (3 - \sqrt{5} )}{ ({3})^{2} - { (\sqrt{5} })^{2} } \: \: [∵ {a}^{2} - {b}^{2} = (a + b)(a - b) ]\\ [/tex]
[tex] = \frac{3 - \sqrt{5} + 3 \sqrt{5} - 5 }{9 - 5} \\ [/tex]
[tex] = \frac{ - 2 + 2 \sqrt{5} }{4} \\ [/tex]
[tex] = \frac{2( - 1 + \sqrt{5} )}{4} \\ [/tex]
[tex] = \frac{ - 1 + \sqrt{5} }{2} \\ [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Mystique35 }}{\red{}}}}}[/tex]
