How do you rationalize the denominator and simplify #1/(sqrt5-3)#?

1 Answer
May 3, 2016

Answer:

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

Explanation:

For expressions #text(something)/(sqrt(a)-b)# we multiply the numerator and denominator by #sqrt(a)+b# so it matches the LHS of the formula #(x+y)(x-y)=x^2-y^2#.

#1/(sqrt(5)-3)=1/(sqrt(5)-3) * (sqrt(5)+3)/(sqrt(5)+3)=(sqrt(5)+3)/(5-9)=-(sqrt(5)+3)/4#