Question 102010
Rationalizing the denominator works as such
{{{ 1 / (sqrt(a) + sqrt(b)) = (1 / (sqrt(a) + sqrt(b))) * ((sqrt(a) - sqrt(b)) / (sqrt(a) - sqrt(b))) = (sqrt(a) - sqrt(b)) / (a - b) }}}

Therefore
{{{ (sqrt(11) - sqrt(5)) / (sqrt(11) + sqrt(5)) }}}
{{{ ((sqrt(11) - sqrt(5)) / (sqrt(11) + sqrt(5))) * ((sqrt(11) - sqrt(5)) / (sqrt(11) - sqrt(5))) }}}
{{{ (sqrt(11) - sqrt(5))^2 / (11 - 5) }}}

Since {{{ (a - b)^2 = a^2 - 2*a*b + b^2 }}}, so
{{{ (11 - 2*sqrt(55) + 5) / (11 - 5) }}}
{{{ (16 - 2*sqrt(55)) / 6 }}}
{{{ (2*(8 - sqrt(55))) / 6 }}}
{{{ (8 - sqrt(55)) / 3 }}}

Hope that helps.