How do you rationalize the denominator and simplify 5/(sqrt[3] – sqrt[5])?

1 Answer
George C.
Mar 17, 2016

5/(sqrt(3)-sqrt(5))=-5/2(sqrt(3)+sqrt(5))

Explanation:

Multiply both numerator and denominator by (sqrt(3)+sqrt(5)):

5/(sqrt(3)-sqrt(5))

=(5(sqrt(3)+sqrt(5)))/((sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))

=(5(sqrt(3)+sqrt(5)))/((sqrt(3))^2-(sqrt(5))^2)

=(5(sqrt(3)+sqrt(5)))/(3-5)

=(5(sqrt(3)+sqrt(5)))/(-2)

=-5/2(sqrt(3)+sqrt(5))

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