How do you simplify $(2-sqrt3)/(-2-sqrt5)$ ?

Question

1432 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-09T12:45:04

See a solution process below:

First, we will rationalize the denominator to remove the radicals from the denominator by multiplying the expression by the necessary form or $1$ :

$(-2 + sqrt(5))/(-2 + sqrt(5)) xx (2 - sqrt(3))/(-2 - sqrt(5)) =>$

$((-2 * 2) + 2sqrt(3) + 2sqrt(5) - sqrt(5)sqrt(3))/((-2 * -2) + 2sqrt(5) - 2sqrt(5) - sqrt(5)sqrt(5)) =>$

$(-4 + 2sqrt(3) + 2sqrt(5) - sqrt(15))/(4 + 0 - 5) =>$

$(-4 + 2sqrt(3) + 2sqrt(5) - sqrt(15))/-1 =>$

$4 - 2sqrt(3) - 2sqrt(5) + sqrt(15)$

Or

$4 - 2(sqrt(3) + sqrt(5)) + sqrt(15)$

How do you simplify (2-sqrt3)/(-2-sqrt5)(2-sqrt3)/(-2-sqrt5)?