How do you rationalize the denominator and simplify ##(sqrt(11)-sqrt(2))/(sqrt(11)+sqrt(2))##?

##(13 -2sqrt(22))/9##
Multiply the numerator and the denominator by the reciprocal of the denominator
##sqrt(11) – sqrt(2)##
This will give you
##(sqrt11 – sqrt2)/(sqrt11 + sqrt2) = (sqrt11 – sqrt2)/(sqrt11 + sqrt2) xx (sqrt11 – sqrt2)/(sqrt11 – sqrt2)##
Then multiply the numerator to each other, same with the denominator to remove the radical sign. Because multiplying the same radicals the result was still the radicand itself
e.
##sqrt 11 xx sqrt 11 = sqrt(11^2) = 121##
The radical expression now become
##(sqrt11 – sqrt2)/(sqrt11 + sqrt2) xx (sqrt11 – sqrt2)/(sqrt11 – sqrt2) = (sqrt11 – sqrt2)^2/(11 – 2)##
This will get you
##(11 – 2 sqrt(22) + 2)/9 = (13 -2sqrt(22))/9##