SOLUTION: 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 exa

Algebra ->  Square-cubic-other-roots -> SOLUTION: 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 exa      Log On


   

Question 396143: Rationalize the denominator. Assume that all expressions under radicals represent positive numbers.
%28sqrt%28r%29-sqrt%28s%29%29%2F%28sqrt%28r%29%2Bsqrt%28s%29%29
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator. Assume that all expressions under radicals represent positive numbers.
%28sqrt%28r%29-sqrt%28s%29%29%2F%28sqrt%28r%29%2Bsqrt%28s%29%29
(Simplify your answer. Type an exact answer, using radicals as needed.)

%28sqrt%28r%29-sqrt%28s%29%29%2F%28sqrt%28r%29%2Bsqrt%28s%29%29
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

%28sqrt%28r%29-sqrt%28s%29%29%5E2%2F%28r+-+s%29 or
%28r+-+2sqrt%28r%29sqrt%28s%29+%2B+s%29%2F%28r+-+s%29