Question

rationalize the denominator √5/√5+2-√3/√5-2

Answer 1

given: √5/√5+2-√3/√5-2

we have to rationalize the denominator

ans: √5(√5-2)-√15(1-2)


see the attachment for further process

___________________________________

Answer 2

hi friend
here's your answer looking for

$\frac{ \sqrt{5} }{ \sqrt{5} - 2} - \frac{ \sqrt{3} }{ \sqrt{5} - 2}$
let's solve it separately

$\frac{ \sqrt{5} }{ \sqrt{5} - 2} = \\ \\ \frac{ \sqrt{5} }{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2}{ \sqrt{5} + 2} = \\ \\ \frac{5 + 2 \sqrt{5} }{5 - 4} = \\ \\ 5 + 2 \sqrt{5}$
now solving second one

$\frac{ \sqrt{3} }{ \sqrt{5} - 2 } \\ \\ = \frac{ \sqrt{3} }{ \sqrt{5} - 2} \times \frac{ \sqrt{5} + 2 }{ \sqrt{5} + 2} = \\ \\ \frac{ \sqrt{15} + 2 \sqrt{3} }{5 - 4} = \\ \\ \sqrt{15} + 2 \sqrt{3}$
now, putting both values

$5 + 2 \sqrt{5} - ( \sqrt{15 } + 2 \sqrt{3} )$
$5 + 2 \sqrt{5} - \sqrt{15} - 2 \sqrt{3}$
hope u r satisfied with my answer