rationalise the denominator and simplyfy (( root (3) + root(2) / root(3) - root(2) )) + (( root(3) - root(2) / root(3) + root(2) ))?

Assuming that meant to read as :-

[ √3 + √2 ] / [ √3 - √2 ] + [ √3 - √2 ] / [ √3 + √2 ]

[ √3 + √2 ] [ √3 + √2 ] + [ √3 - √2 ] [ √3 - √2 ]
--------------------------------------------------------------
[ √3 - √2 ] [ √3 + √2 ]

5 + 2√ 6 + 5 - 2 √6

10

you have [ √3 + √2 ]² +[ √3 - √2 ]² = 3 + 2 + 2√6 - { 3 + 2 - 2 √6] = 4√6

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