Question

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

Answer 1

`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`