Question 1046032
{{{1/((1+sqrt(3))+sqrt(5))}}}

= {{{(1/((1+sqrt(3))+sqrt(5)))*(  ((1+sqrt(3))-sqrt(5))/  ((1+sqrt(3))-sqrt(5))     )}}}

= {{{(1+sqrt(3)-sqrt(5))/( (1+sqrt(3))^2 - 5)}}}

={{{(1+sqrt(3)-sqrt(5))/( 2sqrt(3)-1)}}}

={{{((1+sqrt(3)-sqrt(5))/( 2sqrt(3)-1))( ( 2sqrt(3)+1)/( 2sqrt(3)+1 ) ) }}}

= {{{(2sqrt(3) +1 + 6+sqrt(3) -2sqrt(15) -sqrt(5))/(12-1)}}}

={{{(7 + 3sqrt(3) -sqrt(5) - 2sqrt(15))/11}}}

===> P = 7/11,  Q = 3/11,  R = -1/11, and S = -2/11.