Question

Solve the following surd given below
(1-√5)÷(1+√5)​

Answer 1

`(1-\sqrt 5)/(1+\sqrt 5)\\\\\\=(\left( 1- \sqrt 5\right)\left( 1- \sqrt 5\right))/(\left( 1+ \sqrt 5\right)\left( 1- \sqrt 5\right))\\\\\\=(\left( 1-\sqrt 5)^2)/(1^2 - \left(\sqrt 5 \right)^2)\\\\\\=(1+\left(\sqrt 5 \right)^2 -2 \sqrt 5\cdot 1)/(1-5)\\\\\\=(1+5-2\sqrt 5)/(-4)\\\\\\=-(6-2\sqrt 5)/(4)\\\\\\=-(2\left(3-\sqrt 5 \right))/(4)\\\\\\=-(3-\sqrt 5)/( 2)\\\\\\=(\sqrt 5 -3)/(2)`