SOLUTION: Rationalize the denominator assuming all radicals represent positive numbers. sqrt(c)-sqrt(d) over sqrt(c)+sqrt(d)

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Question 281641: Rationalize the denominator assuming all radicals represent positive numbers.
sqrt(c)-sqrt(d)
over
sqrt(c)+sqrt(d)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


%28sqrt%28c%29-sqrt%28d%29%29%2F%28sqrt%28c%29%2Bsqrt%28d%29%29

Put parentheses around the numerator and denominator

%28%28sqrt%28c%29-sqrt%28d%29%29%29%2F%28%28sqrt%28c%29%2Bsqrt%28d%29%29%29

Form the conjugate of the denominator. that is,
change the sign of the second term of %28sqrt%28c%29%2Bsqrt%28d%29%29,
making it red%28%28sqrt%28c%29-sqrt%28d%29%29%29%29

Now multiply top and bottom of

%28%28sqrt%28c%29-sqrt%28d%29%29%29%2F%28%28sqrt%28c%29%2Bsqrt%28d%29%29%29

by the conjugate red%28%28sqrt%28c%29-sqrt%28d%29%29%29%29




Use FOIL on the top and the bottom:







Combine the middle two terms on top as -2sqrt%28cd%29



Change the sqrt%28c%5E2%29 to just c and sqrt%28d%5E2%29 to just d

%0D%0A%28c-2sqrt%28cd%29%2Bd%29%0D%0A%2F%28c-d%29+

Edwin