Question 190860
{{{(sqrt(5))/(sqrt(5)-1)}}} Start with the given expression



{{{(sqrt(5)(sqrt(5)+1))/((sqrt(5)-1)(sqrt(5)+1))}}} Multiply both the numerator and the denominator by {{{sqrt(5)+1}}}



{{{(sqrt(5)(sqrt(5)+1))/((sqrt(5))^2-(1)^2)}}} FOIL the denominator using the difference of squares formula



{{{(sqrt(5)(sqrt(5)+1))/(5-1)}}} Square each term



{{{(sqrt(5)(sqrt(5)+1))/(4)}}} Combine like terms.



{{{(sqrt(5)*sqrt(5)+1*sqrt(5))/(4)}}} Distribute



{{{(5+sqrt(5))/(4)}}} Multiply



So {{{(sqrt(5))/(sqrt(5)-1)=(5+sqrt(5))/(4)}}}