Question 396143
Rationalize the denominator.  Assume that all expressions under radicals represent positive numbers.
{{{(sqrt(r)-sqrt(s))/(sqrt(r)+sqrt(s))}}}
(Simplify your answer.  Type an exact answer, using radicals as needed.)


{{{(sqrt(r)-sqrt(s))/(sqrt(r)+sqrt(s))}}}
need square roots in denominator to go away,
using conjugate of sqrt(r) + sqrt(s) which is sqrt(r) - sqrt(s)
to multiply numerator and denominator by
use FOIL (First Outer Inner Last) when multiplying
{{{(sqrt(r)-sqrt(s))(sqrt(r)-sqrt(s))/(sqrt(r)+sqrt(s))(sqrt(r)-sqrt(s))}}}
{{{(sqrt(r)-sqrt(s))^2/(r - s)}}} or
{{{(r - 2sqrt(r)sqrt(s) + s)/(r - s)}}}