How do you rationalize the denominator and simplify #3/(2-sqrt5)#?

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Answer 1 · 2017-06-19T20:22:45

When given a fraction of the form:

#c/(a-sqrt(b)#

You rationalize the denominator by multiplying by 1 in the form #(a+sqrtb)/(a+sqrtb)#

Multiply the fraction by 1 in the form #(2+sqrt5)/(2+sqrt5)#:

#3/(2-sqrt5)(2+sqrt5)/(2+sqrt5)#

#(3(2+sqrt5))/(2^2-(sqrt5)^2)#

#(3(2+sqrt5))/(4-5)#

#-3(2+sqrt5)#

#-6-3sqrt5#