Question 195955
{{{2/(sqrt(6)-sqrt(5))}}} Start with the given expression.



{{{(2(sqrt(6)+sqrt(5)))/((sqrt(6)-sqrt(5))(sqrt(6)+sqrt(5)))}}} Multiply both the numerator and denominator by {{{sqrt(6)+sqrt(5)}}}



{{{(2(sqrt(6)+sqrt(5)))/((sqrt(6))^2-(sqrt(5))^2)}}} FOIL the denominator (use the difference of squares formula)



{{{(2(sqrt(6)+sqrt(5)))/(6-5)}}} Square each term.



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



{{{2(sqrt(6)+sqrt(5))}}} Reduce



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



So {{{2/(sqrt(6)-sqrt(5))=2*sqrt(6)+2*sqrt(5)}}}