Question

rationalize the denominator √5-1/√5+1

Answer 1

Hey mate, here is your answer:)

√5-1/√5+1= (√5-1)(√5+1)/(√5+1)(√5+1)

√5-1/√5+1= (√5)^2-(1)^2/5+√5+√5+1

√5-1/√5+1= 5-1/6+2√5

√5-1/√5+1= 4/2(3+√5)

√5-1/√5+1= 2/3+√5

√5-1/√5+1= 2(3-√5)/(3+√5)(3-√5)

√5-1/√5+1= 2(3-√5)/(3)^2-(√5)^2

√5-1/√5+1= 2(3-√5)/9-5

√5-1/√5+1= 2(3-√5)/4

√5-1/√5+1= 3-√5/2


HOPE it helps!!!

Answer 2

$\bf \red{ \underline{Answer:}}$

$\sf \implies \: \frac{ \sqrt{5} - 1 }{ \sqrt{5} + 1 }$

$\sf \implies \: \frac{ \sqrt{5} - 1 }{ \sqrt{5} + 1} \times \frac{ \sqrt{5} - 1 }{ \sqrt{5} - 1}$

$\sf \implies \: \frac{ ({ \sqrt{5} - 1})^{2} }{ {( \sqrt{5} )}^{2} - 1}$

$\sf \implies \: \frac{5 - 2 \sqrt{5} + 1 }{5 - 1}$

$\sf \implies \: \frac{6 - 2 \sqrt{5} }{4}$

$\sf \implies \: \frac{3 - 2 \sqrt{5} }{2}$