Hello Math Community,

I am a 34 year old who hasn't practiced math in a while. I am usually able to help my kiddo with assignments, but I am simply stumped on this problem. I have tried several different ways to research why it's necessary to flip the sign when solving radicals in the denominator, but I am struggling to find answers: I have, 1.) looked in the algebra book, 2.) looked at my kiddo's notes 3.) googled it.

I amnotlooking for a solution to this problem. I am looking to find WHY its necessary to flip the sign to be able to remove the radical from the denominator. Can you help me?

Solve:

(5) / (-5 - 3 * sqrt(3) )

The step that confuses me is the bolded portion below. Why is it appropriate to multiply by a positive 3*sqrt(3) and not the negative 3*sqrt(3) like the denominator in the original expression above?

Solution as determined by my kiddo's notes & photomath's app:

[ (5) *(-5 + 3 * sqrt(3))] / [ (-5 - 3 * sqrt(3) ) *(-5 + 3 * sqrt(3)) ]

Secondly, is there a resource that someone can recommend for me to use on how to solve problems like this? I am a fan of Khan Academy, but I am not sure why topic to search for.

Thank you for your help community.