Question

4 + root under 5/4- under root 5 . simplify

Answer 1

hope you understand this

Answer 2

$\dfrac{4 + \sqrt{5} }{4 - \sqrt{5} }$




$<b>$ By Rationalization, multiply by and divide by ( 4 + √5 )$</b>$


$= > \frac{ 4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ \\ \\ \\ = > \frac{ {(4 + \sqrt{5} )}^{2} }{( 4- \sqrt{5})(4 + \sqrt{5}) }$





On numerator, by formula,
( a + b )² = a² + b² + 2ab


On numerator, by formula,
a² - b² = ( a + b ) ( a - b )


$= > \frac{ {(4)}^{2} + ( \sqrt{5} ) {}^{2} + 2(4 \times \sqrt{5} )}{ {(4)}^{2} - ( \sqrt{5} ) {}^{2} } \\ \\ \\ \\ \\ = > \frac{16 + 5 + 8 \sqrt{5} }{16 - 5} \\ \\ \\ \\ \\ = > \frac{21 + 8 \sqrt{5} }{9}$





Hence, on simplifying ( 4 + √5 ) / ( 4 - √5 ), we get ( 21 + 8√5 ) / 9