Question

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

Answer 1

`= ((1 + √(5)) )/((3 + √(5)) ) \\`

`= ((1 + √(5)) )/((3 + √(5) )) * ((3 - √(5) ))/((3 - √(5)) ) \\`

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

`= (3 - √(5) + 3 √(5) - 5 )/(9 - 5) \\`

`= ( - 2 + 2 √(5) )/(4) \\`

`= (2( - 1 + √(5) ))/(4) \\`

`= ( - 1 + √(5) )/(2) \\`

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