Question

How would I simplify
`(2)/(1+√(5) )` (in simplified radical form) without just turning it into its reciprocal?

Answer 1

`\displaystyle (√(5)-1)/(2)`

Explanation:

`\displaystyle (2)/(1+√(5))\\\\=(2)/(1+√(5))*(1-√(5))/(1-√(5))\\ \\=(2(1-√(5)))/(1-5)\\ \\=(2(1-√(5)))/(-4)\\\\=(√(5)-1)/(2)`