Question 859005
{{{x = sqrt (5) + sqrt (8)}}}


{{{(x+1)/x}}}=?


Plug in {{{sqrt(5)+sqrt(8)}}} in the places of x.


{{{ ( sqrt(5)+sqrt(8)+1 ) / ( sqrt(5)+sqrt(8) ) }}}


Now you want to rationalize the denominator by expanding the fraction with the DIFFERENCE of the roots in the denominator. When you multiply both the top and bottom with {{{sqrt(5)-sqrt(8)}}}, the roots in the denominator will be gone.
Because {{{ ( sqrt(a) + sqrt(b) ) * ( sqrt(a) - sqrt(b) ) = a - b}}}.


So:
{{{ ( (sqrt(5)+sqrt(8)+1) / ( sqrt(5)+sqrt(8) ) ) * ( ( sqrt(5)-sqrt(8) )/( sqrt(5)-sqrt(8) ) )}}}


={{{ ( ( sqrt(5)+sqrt(8)+1 ) * ( sqrt(5)-sqrt(8) ) ) / ( 5-8 ) }}}


When you expand the brackets on the top:


{{{ ( 5 - sqrt(40) + sqrt(40) - 8 + sqrt(5) - sqrt(8) ) / (-3)}}}


The {{{-sqrt(40) + sqrt(40)}}} cancels out and you get:


{{{ ( -3 + sqrt(5) - sqrt(8) ) / (-3)}}}


:) Hope I helped