Question

How do you rationalize the denominator and simplify `(4-2sqrt5)/(6-5sqrt5)`?

Answer 1

`(26-8sqrt5)/89`

Explanation:

Multiply the numerator and the denominator by the conjugate `6+5sqrt5` of the denominator.

Use `(a-b)(a+b)=(a^2-b^2)` to simplify the denominator.

Expand the product in the numerator.

The ratio simplifies to `(26-8sqrt5)/89`