Question

Rationalize:-
1.
$\frac{2}{ (\sqrt3) - ( \sqrt5) }$
and if you know the book name pls tell
and pls solve it is urgent ​

Answer 1

$\sf given : - \frac{2}{ \sqrt{3} - \sqrt{5} } \\ \\ \sf = \frac{2}{ \sqrt{3} - \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \\ \\ \sf = \frac{2( \sqrt{3} + \sqrt{5} )}{( \sqrt{3} - \sqrt{5} )( \sqrt{3} + \sqrt{5}) } \\ \\ \sf = \frac{2( \sqrt{3} + \sqrt{5} )}{( { \sqrt{3}) }^{2} - ( { \sqrt{5} )}^{2} } \\ \\ \sf = \frac{2( \sqrt{3} + \sqrt{5} )}{3 - 5} \\ \\ \sf = \frac{ \cancel2( \sqrt{3} - \sqrt{5} )}{ - \cancel{2}} \\ \\ \sf = - ( \sqrt{3} - \sqrt{5} ) \\ \\ \sf = \boxed{ - \sqrt{3} + \sqrt{5} }$