Question

How do you simplify `(sqrt2-sqrt3)/(sqrt2+sqrt3)`?

Answer 1

See a solution process below:

Explanation:

To eliminate the radicals from the denominator (or to rationalize the denominator) we can multiply the fraction by the appropriate form of `1`. In this case;

`(sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))`

`(sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) + sqrt(3)) =>`

`((sqrt(2))^2 - sqrt(2)sqrt(3) - sqrt(3)sqrt(2) + (sqrt(3))^2)/((sqrt(2))^2 + sqrt(2)sqrt(3) - sqrt(3)sqrt(2) - (sqrt(3))^2) =>`

`(2 - sqrt(6) - sqrt(6) + 3)/(2 + 0 - 3) =>`

`(5 - 2sqrt(6))/(-1) =>`

`-5 + 2sqrt(6)`

Or

`2sqrt(6) - 5`