How do you divide $(sqrt5+1)/(sqrt5-1)$ ?

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Answer 1 · 2015-06-06T23:12:51

Multiply both numerator (top) and denominator (bottom) by the conjugate $(sqrt(5)+1)$ of the denominator:

$(sqrt(5)+1)/(sqrt(5)-1) = (sqrt(5)+1)/(sqrt(5)-1)*(sqrt(5)+1)/(sqrt(5)+1)$

$=(sqrt(5)+1)^2/((sqrt(5))^2-1^2)$

$=(sqrt(5)^2+2sqrt(5)+1)^2/(5-1)$

$=(5+2sqrt(5)+1)/4$

$=(6+2sqrt(2))/4$

$=(2(3+sqrt(5)))/(2*2)$

$=(3+sqrt(5))/2$

How do you divide (sqrt5+1)/(sqrt5-1)(sqrt5+1)/(sqrt5-1)?