Question 94463
Please simplify.
4/the square root of 2-the square root of 6
:
{{{4/((sqrt(2) - sqrt(6)))}}}
:
Multiply by the conjugate of the denominator over itself:
{{{4/((sqrt(2) - sqrt(6)))}}} * {{{((sqrt(2) + sqrt(6)))/((sqrt(2) + sqrt(6)))}}} =
FOIL the denominators, the middle terms cancel
 {{{(4(sqrt(2) + sqrt(6)))/((2 + sqrt(2)*sqrt(6) - sqrt(2)*sqrt(6) - 6))}}} = {{{((4sqrt(2) + 4sqrt(6)))/((2 - 6))}}} = {{{((4sqrt(2) + 4sqrt(6)))/(-4)}}} = {{{(-sqrt(2) - sqrt(6))}}}
Note the -4 cancels and changes the signs