Question 97111
I'm assuming you want to rationalize the denominator right?



{{{6/(3+sqrt(5))}}} Start with the given expression



{{{(6/(3+sqrt(5)))((3-sqrt(5))/(3-sqrt(5)))}}} Multiply the fraction by {{{(3-sqrt(5))/(3-sqrt(5))}}}



{{{6(3-sqrt(5))/(3+sqrt(5))(3-sqrt(5))}}} Combine the fractions



{{{6(3-sqrt(5))/(3*3-3*sqrt(5)+3sqrt(5)-sqrt(5)*sqrt(5))}}} Foil



{{{6(3-sqrt(5))/(3*3+cross(-3*sqrt(5)+3sqrt(5))-sqrt(5)*sqrt(5))}}} Combine and cancel out like terms


{{{6(3-sqrt(5))/(9-5)}}} Multiply



{{{6(3-sqrt(5))/4}}} Combine like terms



{{{3(3-sqrt(5))/2}}} Reduce {{{6/4}}} to {{{3/2}}} (this is probably where you got lost. You should have reduced before you distributed.)



{{{(9-3*sqrt(5))/2}}} Distribute





Check:


Plug in the expression {{{6/(3+sqrt(5))}}} into your calculator to approximately get 1.14589803375031



Now plug in {{{(9-3*sqrt(5))/2}}} into your calculator to approximately get 1.14589803375031


Since they are equivalent, (ie {{{6/(3+sqrt(5))=(9-3*sqrt(5))/2}}}) this verifies our answer