Question

Please help with this
$\frac{3 - \sqrt[]{5} }{3 + \sqrt{5} }$

Answer 1

Hi ,

( 3 - √5 ) / ( 3 + √5 )

Rationalize the denominator ,

= [(3-√5)(3-√5)]/[(3+√5)(3-√5)

= ( 3 - √5 )²/[ 3² - ( √5 )² ]

= [ 3² + ( √5 )² - 2 × 3 × √5 ]/( 9 - 5 )

= ( 9 + 5 - 6√5 ) / 4

= ( 14 - 6√5 ) /4

= [ 2 ( 7 - 3√5 ) ] / 4

= ( 7 - 3√5 ) / 2

I hope this helps you.

: )

Answer 2

hey friend here is your answer ⬇️⬇️☺️

$3 + \sqrt{5} \div 3 - \sqrt{5} \\ = (3 + \sqrt{5} )(3 + \sqrt{5} ) \div (3 - \sqrt{5} )(3 + \sqrt{5}) \\ = (3 + \sqrt{5} )^{2} \div ( {3}^{2} - { \sqrt{5} }^{2} ) \\ = ( {3}^{2} + 2 \times 3 \times \sqrt{5} + { \sqrt{5} }^{2} ) \div (9 - 5) \\ = (9 + 6 \sqrt{5} + 5) \div 4 \\ = 2(7 + 3 \sqrt{5} ) \div 4 \\ = (7 + 3 \sqrt{5} ) \div 2$


hope it helps you ✌️