Question 183015
{{{3/(sqrt(7)-sqrt(2))}}} Start with the given expression.



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




{{{(3(sqrt(7)+sqrt(2)))/((sqrt(7))^2-(sqrt(2))^2)}}} FOIL. Note: the denominator is a difference of squares.




{{{(3(sqrt(7)+sqrt(2)))/(7-2)}}} Square {{{sqrt(7)}}} to get 7. Square {{{sqrt(2)}}} to get 2



{{{(3(sqrt(7)+sqrt(2)))/(5)}}} Combine like terms.



{{{(3*sqrt(7)+3*sqrt(2))/(5)}}} Distribute



So {{{3/(sqrt(7)-sqrt(2))=(3*sqrt(7)+3*sqrt(2))/(5)}}}