Write as:
(5sqrt(10))/(3sqrt(6))+(9sqrt(3))/(3sqrt(6))
=(5sqrt(10)+9sqrt(3))/(3sqrt(6))
Getting rid of the root in the denominator
color(green)(=(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx1)" "->" "(5sqrt(10)+9sqrt(3))/(3sqrt(6))color(red)(xx(sqrt(6))/(sqrt(6))))"
" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(3(sqrt(6))^2))
" "color(green)((5sqrt(10xx6)+9sqrt(3xx6))/(18)
" "color(green)((5sqrt(2xx5xx2xx3)+9sqrt(3xx3xx2))/(18)
" "color(green)((10sqrt(15)+27sqrt(2))/(18)
" "color(green)((5sqrt(15))/9+(3sqrt(2))/2)