Question

(1+√5)/(3+√5) Surs and need all working as I do not know how to do this at all

Answer 1

$= \frac{(1 + \sqrt{5}) }{(3 + \sqrt{5}) }$

$= \frac{(1 + \sqrt{5}) }{(3 + \sqrt{5} )} \times \frac{(3 - \sqrt{5} )}{(3 - \sqrt{5}) }$

$= \frac{1(3 - \sqrt{5}) + \sqrt{5} (3 - \sqrt{5} )}{ ({3})^{2} - { (\sqrt{5} })^{2} } \: \: [∵ {a}^{2} - {b}^{2} = (a + b)(a - b) ]$

$= \frac{3 - \sqrt{5} + 3 \sqrt{5} - 5 }{9 - 5}$

$= \frac{ - 2 + 2 \sqrt{5} }{4}$

$= \frac{2( - 1 + \sqrt{5} )}{4}$

$= \frac{ - 1 + \sqrt{5} }{2}$

$\large\mathfrak{{\pmb{\underline{\red{Mystique35 }}{\red{}}}}}$