Question

Simplify 1/(sqrt(5) + sqrt(2)) + 1/(sqrt(5) - sqrt(2))​

Answer 1

Answer:

2√5/3

Step-by-step explanation:

$\frac{1}{ \sqrt{5} + \sqrt{2} } + \frac{1}{ \sqrt{5} - \sqrt{2} }$

$\frac{ \sqrt{5} - \sqrt{2} + \sqrt{5} + \sqrt{2} }{ (\sqrt{5} + \sqrt{2})( \sqrt{5} - \sqrt{2} ) }$

$\frac{2 \sqrt{5} }{ { \sqrt{5} }^{2} - { \sqrt{2} }^{2} }$

$\frac{2 \sqrt{5} }{5 - 2}$

$\frac{2 \sqrt{5} }{3}$

Answer 2

Step-by-step explanation:

√ 5 - √ 2 + √ 5+√2

= --------------------------------

√5+√2 √5-√2

=2√5/5-2

=2√5/3