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

1 Answer
May 3, 2016

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