Question 167726
{{{7/(sqrt(3)-sqrt(2))}}} Start with the given expression



{{{(7/(sqrt(3)-sqrt(2)))((sqrt(3)+sqrt(2))/(sqrt(3)+sqrt(2)))}}} Multiply both numerator and denominator by the conjugate of the denominator



{{{(7(sqrt(3)+sqrt(2)))/((sqrt(3)-sqrt(2))(sqrt(3)+sqrt(2)))}}} Combine the fractions.




{{{(7(sqrt(3)+sqrt(2)))/((sqrt(3))^2-(sqrt(2))^2)}}} FOIL (hint: use the difference of squares)



{{{(7(sqrt(3)+sqrt(2)))/(3-2)}}} Square each value



{{{(7(sqrt(3)+sqrt(2)))/(1)}}} Combine like terms.



{{{7(sqrt(3)+sqrt(2))}}} Simplify



{{{7*sqrt(3)+7*sqrt(2)}}} Distribute



So {{{7/(sqrt(3)-sqrt(2))=7*sqrt(3)+7*sqrt(2)}}}