Question 147682

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



{{{(5/(sqrt(3)+sqrt(5)))((sqrt(3)-sqrt(5))/(sqrt(3)-sqrt(5)))}}} Multiply both the numerator and denominator by the conjugate of the denominator {{{sqrt(3)-sqrt(5)}}}.



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



{{{(5(sqrt(3)-sqrt(5)))/(3-5)}}} Foil the denominator.



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



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



So {{{5/(sqrt(3)+sqrt(5))}}} simplifies to {{{(5*sqrt(3)-5*sqrt(5))/(-2)}}}



In other words, {{{5/(sqrt(3)+sqrt(5))=(5*sqrt(3)-5*sqrt(5))/(-2)}}}