Question

How do you rationalize the denominator and simplify `1/(1+sqrt(3)-sqrt(5))`?

Answer 1

`(7+3sqrt3+sqrt5+2sqrt15)/11` = 2.0162, nearly.

Explanation:

Multiply numerator and denominator by `(1+sqrt3+sqrt5)`.
Use `(a+b)(a-b)=(a^2-b^2)` for the denominator.

The denominator now is `(1+sqrt3)^2-(sqrt5)^2= 2sqrt3+1`.

Multiply the numerator and denominator by the conjugate `2sqrt3+1` of the denominator.

Now, the denominator is rationalized to 11.

Expand the product in the numerator and simplify for the answer.

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