Question

1/√5 +√2 + 1/√5 - √2

Answer 1

1/(√5+√2.)+ 1/(√5-√2)

=√5-√2+√5+√2/(√5+√2)*(√5-√2)

=2√5/(5-2)

=(2√5)/3

Answer 2

$\frac{1}{ \sqrt{5} + \sqrt{2} } + \frac{1}{ \sqrt{5} - \sqrt{2} } \\ = \frac{ \sqrt{5} - \sqrt{2} + \sqrt{5} + \sqrt{2} }{( \sqrt{5} + \sqrt{2})( \sqrt{5} - \sqrt{2} ) } \\ = \frac{2 \sqrt{5} }{( { \sqrt{5}) }^{2} - ({ \sqrt{2}) }^{2} } \: \: ( {x}^{2} - {y}^{2} ) \\ = \frac{2 \sqrt{5} }{5 - 2} \\ = \frac{2 \sqrt{5} }{3}$