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

1 Answer
Mar 17, 2016

Answer:

#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))#