Question

Date
Pege
Simplify
+
:-
J5+3
Į (JS-13)​

Answer 1

Answer:

root 5 - root 3

Step-by-step explanation:

$\frac{1}{ \sqrt{5} + \sqrt{3} } + \frac{1}{2} ( \sqrt{5} - \sqrt{3} ) \\ = \frac{1}{ \sqrt{5 }+ \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{2} \\ = \frac{2 + ( \sqrt{5 } + \sqrt{3} )( \sqrt{5} - \sqrt{3} )}{2( \sqrt{5} + \sqrt{3}) } \\ = \frac{2 + { \sqrt{5} }^{2} - { \sqrt{3} }^{2} }{2( \sqrt{5} + \sqrt{3} )} \\ = \frac{2 + 5 - 3}{2( \sqrt{5} + \sqrt{3} ) } \\ = \frac{4}{2( \sqrt{5} + \sqrt{3} )} \\ = \frac{2}{ (\sqrt{5} + \sqrt{3} )} \\ = \frac{2}{( \sqrt{5} + \sqrt{3} } \times \frac{( \sqrt{5} - \sqrt{3} ) }{( \sqrt{5} - \sqrt{3}) } \\ = \frac{2( \sqrt{5} - \sqrt{3} ) }{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } \\ = \frac{2( \sqrt{5} - \sqrt{3} )}{5 - 3} \\ = \frac{2( \sqrt{5} - \sqrt{3} ) }{2} \\ = \sqrt{5} - \sqrt{3}$