1. ## rationalize the denominator

Hi all,

First of all hello! I am new here. Nice to meet you.

I am taking an algebra class this semester after a very long break from math. I'm having a little trouble remembering some things and so far reading my textbook hasn't been very helpful.

I have a problem that says "rationalize the denominator" and the problem is:

3 + √x / 3 - √x

I have come up with several different answers and I just need to know if I am on the right track. I multiplied both sides of the expression by the inverse of the denominator and used the FOIL method. I came up with 10√x^4 / √x^2 the last time I worked this expression out. Am I doing this correctly?

2. Originally Posted by uglygreencouch
Hi all,

First of all hello! I am new here. Nice to meet you.

I am taking an algebra class this semester after a very long break from math. I'm having a little trouble remembering some things and so far reading my textbook hasn't been very helpful.

I have a problem that says "rationalize the denominator" and the problem is:

3 + √x / 3 - √x

I have come up with several different answers and I just need to know if I am on the right track. I multiplied both sides of the expression by the inverse of the denominator and used the FOIL method. I came up with 10√x^4 / √x^2 the last time I worked this expression out. Am I doing this correctly?
to rationalize the denominator, you multiply by its conjugate over itself (so it's like multiplying by 1 so you don't change anything). that is, the same expression but you change the sign in the middle

So you do the following:

$\frac {3 + \sqrt {x}}{3 - \sqrt {x}} = \frac {3 + \sqrt {x}}{3 - \sqrt {x}} \cdot \frac {3 + \sqrt {x}}{3 + \sqrt {x}}$

Can you take it from here?

3. I'm a little worried about the word "inverse". I was hoping for "conjugate".

The idea of rationalization is this: (a+b)(a-b) = a^2 - b^2 If a or b are square roots, this gets rid of the radicals. If you end up with some radicals, something went wrong.

$(3-\sqrt{3})(3+\sqrt{3}) = 3^{2} - (\sqrt{3})^{2} = 9 - 3 = 6$

4. I see what I was doing wrong! Thank you so much. I will learn this stuff if it kills me!