Question 866633
{{{(4+sqrt(5))(sqrt(5) -3)/(2-sqrt(5))}}}
First, use FOIL to multiply {{{(4+sqrt(5))(sqrt(5) -3)}}}
{{{(4sqrt(5)-3sqrt(5)-12+5)/(2-sqrt(5))}}}
{{{(sqrt(5)-7)/(2-sqrt(5))}}}
Multiply the expression by the conjugate of the denominator
{{{(sqrt(5)-7)(2+sqrt(5))/(2-sqrt(5))(2+sqrt(5))}}}
Multiply
{{{(5-7sqrt(5)+2sqrt(5)-14)/(4-sqrt(5)^2)}}}
Simplify
{{{(-5sqrt(5)-9)/-1}}}
Cancel out -1
{{{sqrt(5)+9}}}