Question

$1 \div (\sqrt{2} + \sqrt{3} - \sqrt{5} ) + (1 \div ( \sqrt{2} - \sqrt{3} - \sqrt{5} )$
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Answer 1

Left hand side

(r = root)

=1/r2+r3-r5 × r2-r3+r5/r2-r3+r5

=r2-r3+r5/2-r6+r10+r6-3+r15-r10+

r15-5

=r2-r3+r5/-6+2r15

Right hand side

=1/r2-r3-r5 × r2+r3+r5/ r2+r3+r5

=r2+r3+r5/2+r6+r10-r6-3-r15-r10-r15-5

=r2+r3+r5/-6-2r15

Add both

=r2+r3+r5/-6-2r15 + r2-r3+r5/-6+2r15