How do you rationalize the denominator and simplify #3/(4+4sqrt5)#?

1 Answer
Sep 26, 2015

Answer:

Multiply both numerator and denominator by #(sqrt(5)-1)# and rearrange to find:

#3/(4+4sqrt(5)) =(3sqrt(5)-3)/16#

Explanation:

Using the identity #a^2-b^2 = (a-b)(a+b)# we find:

#3/(4+4sqrt(5))#

#=3/(4(1+sqrt(5))#

#=3/(4(sqrt(5)+1)#

#=3/(4(sqrt(5)+1))*((sqrt(5)-1))/((sqrt(5)-1))#

#=(3(sqrt(5)-1))/(4(sqrt(5)-1)(sqrt(5)+1))#

#=(3(sqrt(5)-1))/(4((sqrt(5))^2-1^2))#

#=(3(sqrt(5)-1))/(4(5-1))#

#=(3(sqrt(5)-1))/16#

#=(3sqrt(5)-3)/16#