Question 118145

{{{(2)/(sqrt(6)-sqrt(5))}}} Start with the given expression



{{{((2)/(sqrt(6)-sqrt(5)))((sqrt(6)+sqrt(5))/(sqrt(6)+sqrt(5)))}}} Multiply by the fraction by {{{(sqrt(6)+sqrt(5))/(sqrt(6)+sqrt(5))}}}. Note  {{{sqrt(6)+sqrt(5)}}} is the conjugate of {{{sqrt(6)-sqrt(5)}}}.



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



{{{(2)(sqrt(6)+sqrt(5))/(sqrt(6)*sqrt(6)+(sqrt(6))(sqrt(5))-sqrt(6)sqrt(5)+(-sqrt(5))*(-sqrt(5)))}}} Foil the denominator



{{{(2)(sqrt(6)+sqrt(5))/(sqrt(6)*sqrt(6)+(-sqrt(5))*(-sqrt(5)))}}} Cancel like terms



{{{((2)(sqrt(6)+sqrt(5)))/(6-5)}}} Multiply


{{{((2)(sqrt(6)+sqrt(5)))/(1)}}} Combine like terms



{{{(2)(sqrt(6)+sqrt(5))}}} Remove the denominator of 1



{{{2*sqrt(6)+2*sqrt(5)}}} Distribute